I have a couple of basses with that sound, (Jerry Jones, Multivox Marvel) but none of them are practical or cheap alternatives to a vintage H22.
You could look for a Value Leader or similar cheap Kay model with speed bump pickups. They can still be had occasionally at reasonable prices. The tuners are no better than a Harmony (or any other cheap old bass) but that is just the reality of these instruments. You can have Hipshot guitar tuners (certain models, not all) bored out to accept bass strings for a very modest upcharge. I have them on my Multivox and it is really the only way to go.
I also think (*unpopular opinion alert*) that the hollowness of the body has little to do with the sound, relative to pickup type/placement and the bridge.
I feel like you could mount a gold foil pickup in a Squier vintage tele bass where the humbucker is, (on a hollow block, if you like), make some wooden bridge saddles a la Guild basses, and THAT would get you 90% there. Cheap, but some DIY involved…
I haven't done this, so I could be wrong.
I wouldn't rule out basses with a center block, or even a solid body.
The bass doesn't need to be a shortscale, but it definitely doesn't hurt.
But a single coil next to the neck, and some sort of natural muting/decay by the bridge is key.