The main issue with my 96 gs500e is a consistent carbon foul on the left spark plug. took the carb out and cleaned it out and found a bad float needle. Replaced it and bike seemed okay. About 100 miles later, I wasn't able to get up hills and found the left spark plug had fouled again. All that was done was seafoam in the gas tank to clean out the tank and carb and a fuel filter spliced from the petcock to the carb. The fuel air mixture screws are at 2.5 turns out.

I am also planning on doing a carb sync with a homemade manometer today.

Any help would be greatly appreciated.

Also:

Put in a new spark plug and started the bike up. Took off the right spark plug cap to see if it was good -- idle drops and eventually dies. If I take off the left cap, bike idles normally.

Does the plug look like this, or worse / different?  (Image from Haynes manual)

yeah it looks like that but not so bad around the threads.

I have left my carbs bone-stock, so I don't have much experience with the fuel-air mixture screws ... but the next item on my To-Do list would be to try some different "turns out" settings on the left carb.  Thinking through the possible issues mentioned in the graphic...

       Caused by an over-rich fuel/air mixture, faulty choke operation or blocked air filter.

... the "blocked air filter" would affect both cylinders, right?

Each carburetor does have its own "choke" circuit, so I suppose the left one could be "faulty" ... but since you mentioned the number of turns on the screws I assume you have actually adjusted/checked them yourself.

Would it be fairly easy to try a few different fuel-air screw settings for the left carb?

First thing, check to see if you are getting a strong and regular spark in that cylinder.  If the fuel isn't burning, the plug will look like that.

Also check the float level settings.  There is a video on this web site how to do it.  It involves 1/4" clear aquarium tubing.  If the float level in that carb is set too high, no amount of screw turning or jet replacing will fix your problem.  You would have to set the float to the proper height.