You have to start by getting a good rendering of Matthew 5:32. You do NOT. (Even the Greek makes it obvious, as has been discussed here on this forum, conservatively, 100 times.
And has been pointed out, you ignore the clear text of Deuteronomy 24:1-3, repeatedly.
I can see that the main point of contention is the significance of the divorce certificate. And, there is none.
By definition, only men could get a divorce. Divorce is something that a woman simply could not initiate, so of course it would only be logical, then, to require a man to give a woman proof that she wasn't the one who ran off, but the man who sent her away. There is absolutely no more to the divorce certificate than that.
What is being ignored by several, rather, is that the divorce with the certificate is not enough to cause the first marriage to rejoin. Only after a second marriage does the law of Deut 24:1-4 apply, and at that point, the law says the the woman has been "defiled."
The other point that I see this mindset ignoring is that, divorce certificate or not, the divorces that Moses permitted were not desired by God (Matthew 19:8-9). At the very least, if a woman had merely been given a certificate and sent away, not having yet married another man, then they could indeed come back together. Therefore, you cannot say about a second marriage, "what God has joined together, let no man separate" when in reality it's the first marriage that God would have be restored.