Have a 2005 Craftsman 1000 with an 18 hp Briggs and Stratton engine. Can't figure where to start to resolve my problem. Once I hand push the mower to a level or uphill situation, I can start the engine and it will run until I again get into a right hand tilt position. Checked and ordered a seat "kill" switch because the wings that secure it to plate have become untenable. But I don't think that is really the problem here though, I was able to run the mower with the switch depressed in my hand. Still at a loss to resolve the stalling problem. Help!

How much fuel is in the tank and is there any debris in the tank?

Scleros could b onto something but I'd also continue looking at the kill switch. There is freequently enough wire in the harness to detact the switch and hold it closed while riding on this hill, that would tell you if it's the switch or the mount. In the meantime, top off the tank.