Sounds like your main jet is partly plugged up and the fuel pump is weak.
I just put a carb and fuel pump kit in my Craftsman II GT18 and a new starter gear on the starter.Sounds like your having the exact same problem that I was having.
This is the Kit that I got.Complete with Fuel pump rebuild kit.
I have a '88 or '89 Sears with Twin Briggs, did the same thing. It got to the point carb was so clogged wouldn't even hardly run with choke on. I bought rebuild kit for like $20-25 and she runs pretty well now.
I put a new fuel line filter on (start back and work my way up) and no luck. Cleaned off the outside of carb to see what I could see. In the closest manual available(my guess) the 917.255915 the carb looks to be identical as the engine model numbers are the same as mine. So a rebuild kit will be next in line. Might get it local if I can and when I get to it I will make a report. In the meantime, it was mentioned the main jet was clogged. Will I need to disassemble to check this? I've never rebuilt a carb and don't want to mess anything up.