You've spent a lot a that shop for questionable results. Given the resources you'll find on this site, I'd take a break from those guys for a while. Stripped screws on new hardware, guesses about what it might still be... IMO They're getting paid by you to experiment on your bike.
A very good place to start is to download the service/workshop manual for your bike:
http://manuals.sohc4.net/cb750k/It's in multiple PDF's, don't forget the supplements, don't forget the wiring diagrams, etc. I have printed copies in 3-ring binders for each of my bikes and I use them frequently.
As to the problems you're experiencing, take a systematic approach, break it down into components starting at the beginning (the inputs - air, fuel & spark). Think about the system and think about the symptoms. There are inputs that affect all carbs or all cylinders one at a time, in pairs, or all at once.
You need to make sure you're in a good starting position.
Refer to Part 6 of the workshop manual, page 172 according to the printed numbers, page 3 in the PDF. This is where you find the correct procedure for the compression test. Also check page 181 for valve adjustment. Basically, you need to go through the items in the 3000-mile service checklist (p. 176-177) to get yourself in a base starting position from which you can make intelligent tests and adjustments. (Obviously the things like spokes and turn signals can wait...) That lack of smooth running can definitely be a symptom of timing. You'll have to get that sorted, too (p. 180).
Then you can start making adjustments to target the sootiness in cylinder 1. Maybe you can make an extra 1/2 turn out on the #1 carb to add air to reduce the rich condition. Clean the spark plug or use one of your spares (You did check that the plug gap is set correctly, yes? page 179). Maybe the air screw changes don't have any impact. At that point start looking for air leaks, and check that the carb floats are set to the right height (p. 249 of the K1-K8 workshop supplement, 26mm. Also where you find the correct starting position for the air screws: "1 turn out +/-1/8".)
The point is, get to a good starting point, make one change at a time, and you'll make improvements. Keep a notebook, write down every change, what the symptoms were, etc. Again, I have one of these for every bike.
Plus post your progress. There are lots of people here to help.
Good luck!