Ethan - the coil is new but what about the other basic stuff, like the points, condenser and spark plug?
The first thing I'd do myself is check the timing - and that would be using a timing light. The ole .020 points setting using a feeler gauge (or going way back, using a match book cover) is just the starting point. It's usually close enough to get the engine started but I've found over the years that .022 or .023 is generally more accurate for exact timing, and then there are those engines where it's about .018.
Once you know the timing is accurate, you've got a good spark plug, and good fuel - if it still have the problem I'd re-check the carb settings, make sure the governor is set correctly, make sure your throttle spring is in the correct holes and isn't starting to break or binding, AND if you still have the problem I'd be trying to check out the muffler to make sure it isn't partially blocked.
The backfire you mentioned made me think the muffler might be partially blocked - you could take it off and attempt to dump any loose crud out of the inlet hole. (Guess it would be easy enough to just do this first instead of the timing and other things I mentioned).
After all this then I might just go thru the carb for the sake of doing it - but usually the carb either operates fine or if there is a problem it's a problem all the time.
And finally, if none of this helps, I'd try a different known good coil even tho the one you got is new. Most of the coils ain't made in the good ole U.S.A. these days and don't hold up like the good ones did.
Keep us informed of how you make out.