Spent some more time with it after work, yesterday. I pulled the spark plug, to make sure it's getting spark (it is). I pulled and disassembled the carburetor and it was totally clean inside, jets clear/open. It gets gas to the carb, I can feel it suck air when you pull the cord (it'll suck my palm against the air filter if I put my hand up against it) and you can also hear what I always assumed were the reed valves quack at the end of the spin. It did start one time out of many, many pulls, but just ran a couple seconds and I couldn't get it to stay alive with the primer. By the way, that's how it usually was; it would start and then try to die and you could get it to surge back up by pressing the primer once. Typically, you'd have to do that 1-5 times before it'd level off and run on its own, but now it won't really even start.
So what's next? Should I buy a compression gauge and see if I'm wasting my time? Am I being dumb in overlooking something?