Providing the Sears 917.xxxxxx number would allow one to see more specific details such as-
Does the engine have a fuel pump or is it gravity flow etc.

I'm simply not going approach 2 different directions at the same time when I know one is a total waste of time.

Craftsman Lawn Tractor
#917.28910
Electric Start
Auto Trans.
20hp
42" mower deck
Mower will run untill gas tank is 1/2 to 2/3rds full and then quits. if I fill it back up to completely full it runs fine, but it won't use all the gas in the tank. What good is it to have a big tank if it won't use all the fuel?

The engine in that according to Sears is a Briggs 331877-0946-B1

However, when I plug that number into the Briggs website, it doesn't come up????
Could you verify the engine Model & Type?

In the meantime, I'll suggest this approach-
Tank venting.
After mowing about 1/2 until your expected "stall time", loosen the gas tank cap for a few seconds and then continue mowing. See how long it takes until it does stall. That should give an indication if it's a venting issue, or a possible?? fuel pump issue.

You could also look at the tank location. IS IT a true Gravity Feed tank?
OR
Look on the engine for a fuel pump.
It'll be connected to the carb with one line, the tank with one line and a 3rd line will be a vacuum pulse line going to the crankcase breather.

Let us know what set up you have.
(Venting could also affect a fuel pump engine)