Another way of handling the huge "Jon taken prisoner instead of being killed immediately" plothole

I like that - much better than what they gave us.

That would have worked as an alternative scene to the one they chose. It could have perhaps prevented the schism that threatened to emerge afterwards as a result of Jon's action.

But the script needed Jon to be in prison so Tyrion could make Bran king. How would he be in prison if the Dothraki and Unsullied accepted Jon's authority?

No, no, no it is much better to just cut away from the scene and let the audience fill in the important details on the sensibility of the next scene. The audience is great at filling in the details themselves; just ask J.J. Abrams.

Yeah, Grey Worm and the Unsullied were slaughtering soldiers who had surrendered without a second thought or hesitation, so it makes perfect sense that they wouldn't kill Jon after murdering Dany and just take him prisoner for a trial of some sort.

Better than what they actually did. Greyworm letting him live is inexplicable, especially after earlier in that very same episode it was established that he would ruthlessly kill anyone who stood against Dany, If he would do that, certainly he would have killed Jon. With Drogon, can make the case that since Jon is a dragonrider and a Targ, Drogon won't attack him.