I'm going to differ with @IshChayil regarding the likely scenario here - but ultimately, either way, Moses was clearly a polygamist regardless, all lines of reasoning end up with that conclusion!
There is clearly a large gap in Moses' life (between adoption by the princess and banishment at 40 years of age) that is not directly addressed in scripture. Acts 7:22 shows that something interesting happened there, for him to be "mighty in his deeds". You can't live your entire young adult life as a prince and not end up doing something interesting - and God would have been using every part of his life to train him in various skills he would need to later lead the Israelites. In that context, Josephus' account is entirely plausible. It's exactly the sort of thing that you can imagine God doing with him, as perfect training for later leadership of Israel both through the desert and in war. It would also help to explain the respect everyone had for him - a random guy can't just turn up and tell a nation "listen to me", can't get an audience with Pharoah, can't try and tell the ruler what to do without instantly being beheaded for insolence. Sure, it could have all been just because he was adopted by the princess, but respect for past deeds does make this make a bit more sense.
I try to minimise speculation. If a well-regarded historian has recorded a plausible series of events, that does not contradict scripture, and I have no other very solid evidence countering it, then I'll accept that is probably correct. I know full well that Josephus may well have had incomplete information, he may have filled in some gaps with his own imagination, he may have embellished it here and there. It's most likely partially factual and partially speculative - but I have no idea which bits are which. If I throw out the entire account and make up my own hypothesis, I know I'm probably throwing away facts. And I can't pick and choose and guess which bits are the facts, I'll probably still throw out facts. Josephus, having studied this in detail and having access to far more records than I do, was far more qualified to speculate and fill in the gaps. And he's already done that for me. So I just accept that his account, even if flawed, is more accurate than anything I'm likely to come up with, and run with it as the most likely scenario.
Also, regarding polygamy, I highly doubt that Israel would have given it up under Egyptian rule. We're talking about a nation that came from a man with four wives, whose entire identity is built around the fact that he had 12 sons who became the tribes. This is all very recent family history at the time. Anyone wanting to emulate their forefathers would be thinking of polygamy as one of the key aspects of Jacob's life. They would have been influenced by Egyptian culture, and the rate of polygamy may have reduced, it may even have been hidden as many native African Christians do today (they are polygamous as per their culture but don't tell the church so they don't get kicked out). But what does scripture actually indicate?
It sounds like they were using marriage arrangements that meant that regardless of how many men were killed off, every potential childbearing woman could still be utilised to her full breeding capacity.
Finally, regarding Miriam's objection specifically, the wife being objected to is specifically identified as an Ethiopian, and this is considered such an important point it is stated twice. If Miriam was upset about polygamy, would this not more likely say "Miriam and Aaron spoke against Moses because of the second woman whom he had married; for he had married a second woman." Why repeat a fact that is irrelevant, and not mention what Miriam was actually upset about? And why would she get so upset about Moses, as leader of the nation, simply emulating Jacob, the forefather of the entire nation? Could anybody in that time logically object to the leader of a nation being a polygamist, when the kings of most nations had harems? It's one possibility, but far from the most likely, there are so many reasons to question it.
I think she was most likely upset about Moses' wife's race, simply because that is what scripture actually talks about. The simplest answer is most likely to be correct. Anything else is more speculative.
All this is splitting hairs. It's still clear Moses was a polygamist! But if I decide to spend hours pondering every unimportant detail of the matter, this is where I end up...
There is clearly a large gap in Moses' life (between adoption by the princess and banishment at 40 years of age) that is not directly addressed in scripture. Acts 7:22 shows that something interesting happened there, for him to be "mighty in his deeds". You can't live your entire young adult life as a prince and not end up doing something interesting - and God would have been using every part of his life to train him in various skills he would need to later lead the Israelites. In that context, Josephus' account is entirely plausible. It's exactly the sort of thing that you can imagine God doing with him, as perfect training for later leadership of Israel both through the desert and in war. It would also help to explain the respect everyone had for him - a random guy can't just turn up and tell a nation "listen to me", can't get an audience with Pharoah, can't try and tell the ruler what to do without instantly being beheaded for insolence. Sure, it could have all been just because he was adopted by the princess, but respect for past deeds does make this make a bit more sense.
I try to minimise speculation. If a well-regarded historian has recorded a plausible series of events, that does not contradict scripture, and I have no other very solid evidence countering it, then I'll accept that is probably correct. I know full well that Josephus may well have had incomplete information, he may have filled in some gaps with his own imagination, he may have embellished it here and there. It's most likely partially factual and partially speculative - but I have no idea which bits are which. If I throw out the entire account and make up my own hypothesis, I know I'm probably throwing away facts. And I can't pick and choose and guess which bits are the facts, I'll probably still throw out facts. Josephus, having studied this in detail and having access to far more records than I do, was far more qualified to speculate and fill in the gaps. And he's already done that for me. So I just accept that his account, even if flawed, is more accurate than anything I'm likely to come up with, and run with it as the most likely scenario.
Also, regarding polygamy, I highly doubt that Israel would have given it up under Egyptian rule. We're talking about a nation that came from a man with four wives, whose entire identity is built around the fact that he had 12 sons who became the tribes. This is all very recent family history at the time. Anyone wanting to emulate their forefathers would be thinking of polygamy as one of the key aspects of Jacob's life. They would have been influenced by Egyptian culture, and the rate of polygamy may have reduced, it may even have been hidden as many native African Christians do today (they are polygamous as per their culture but don't tell the church so they don't get kicked out). But what does scripture actually indicate?
The Israelites were breeding like rabbits, within a few generations of immigrating they were starting to outnumber the Egyptians. So they were persecuted by killing off males. We all know the result, in Exodus 7:20: "...the people multiplied, and waxed very mighty." Just as before. Killing the males doesn't appear to have greatly changed the population growth rate.Exodus 1:7-9 said:And the children of Israel were fruitful, and increased abundantly, and multiplied, and waxed exceeding mighty; and the land was filled with them.
Now there arose up a new king over Egypt, which knew not Joseph.
And he said unto his people, Behold, the people of the children of Israel are more and mightier than we:
It sounds like they were using marriage arrangements that meant that regardless of how many men were killed off, every potential childbearing woman could still be utilised to her full breeding capacity.
Finally, regarding Miriam's objection specifically, the wife being objected to is specifically identified as an Ethiopian, and this is considered such an important point it is stated twice. If Miriam was upset about polygamy, would this not more likely say "Miriam and Aaron spoke against Moses because of the second woman whom he had married; for he had married a second woman." Why repeat a fact that is irrelevant, and not mention what Miriam was actually upset about? And why would she get so upset about Moses, as leader of the nation, simply emulating Jacob, the forefather of the entire nation? Could anybody in that time logically object to the leader of a nation being a polygamist, when the kings of most nations had harems? It's one possibility, but far from the most likely, there are so many reasons to question it.
I think she was most likely upset about Moses' wife's race, simply because that is what scripture actually talks about. The simplest answer is most likely to be correct. Anything else is more speculative.
All this is splitting hairs. It's still clear Moses was a polygamist! But if I decide to spend hours pondering every unimportant detail of the matter, this is where I end up...