The good news is that I got the bandsaw blade aligned and tense enough that I was able to make a straight, non-barreled cut. The bad news is when I tried to cut a fairly mild cut, the blade snapped.
The mitigating news is that when a bandsaw blade snaps, the wheels are not longer able to move it because the tension is gone, so it just stops moving.
I’m not sure how much more I should put into this particular bandsaw, but if I do get a new blade, I can just use it on another bandsaw if I ditch this one.