Carb issue

The key to setting fuel/air mixture is by looking at the colour of the spark plug. A general guideline for mixture is to start at 2 1/2 turns out and tweak it from there, however....

IF your carb kit is an aftermarket Chinese, eBay, Amazon etc item then it stands a very good chance of never running right.

Can you post a photo of your spark plug?

Okay, the OEM carb is the one to stick with for sure.
Is the enrichment valve stuck at all or is the seal perished? That could cause you issues. The mixture screw if I remember rightly is on the bottom of the carb just infront of the float bowl, it’s been a while since I rebuilt a 250 carb but I’m sure that’s it’s location.
IN will lean the mixture, OUT will richen the mixture. Do you know how many turns out you are already?

Yes that’s it. So 2.75 out is probably to much, hence the black smoke your experiencing, usually you’d be between 2 1/4 to 2 1/2 turns out.
Highest rpm isn’t quite right, you’ll screw in until idle starts to lower, then out until idle starts to raise and then find the middle ground, that would be the correct procedure. Usually works out at 2 1/2 out though as I said