The saw ended up being in pretty good shape, it just needed tons of cleaning. I took the entire band saw apart down to the nuts and bolts, cleaned it, and re-assembled it. The wheel bearings were in decent shape. I re-packed one of the bearings with grease since the original grease had fossilized.
The original table insert had gone missing and a replacement insert costs more than I think it's worth so I made my own using a fly cutter on my drill press to cut a circular insert out of one-eighth inch hardboard.
The only thing that truly needed to be replaced was the band saw tires, since they were both in some state of disintegration. The motor belt was a bit worn which I suspect was adding some additional vibration to the machine, so I replaced it as well. Even the blade wasn't in terrible shape.
The final report is that it cuts pretty well even up to around 4" thick wood. I haven't tried anything thicker yet, but the motor doesn't seem to strain. All told I spent about $30 in parts. Not bad for a decent band saw.
I did eventually invest in a 3tpi blade to try out the re-saw capability. The new blade cuts through wood like butter; now I just need to make a resawing sled so I can start to saw small logs into boards. But that is a post for another day...