"Surely the muffler produces enough pressure to push the fuel through?"
No. Muffler pressure is not a pump. It reaches a point where the tank is pressurized and the muffler can not pressurize it any further. And keep in mind that pressure setting changes with every throttle change. Higher throttle = higher velocity exhaust = higher tank pressure.
The pressure in the tank can not increase any more no matter what the attitude of the aircraft. So if you're in an upline then the tank doesn't become more pressurized and gravity makes it harder for the engine to draw fuel.
Using tank pressure or not you have to set you engine richer to keep running in all flight attitudes.
Normally what people do is hold their airplane vertically, peak the engine and then back it off a couple clicks. That's very close to an optimum setting for most sport planes. Fly some maneuvers and make small adjustments if there are any problems.
For me that usually means going just a hair richer than originally set because I don't back off the needle enough when holding the plane vertically hoping that it will work out and I'll have just that tiny bit more power. After a single flight I richen it up and usually it's good to go assuming the engine is broken in.