I bought a Teisco Tulip bass a while back for my daughter. Like many of them, the neck is just off center, but it's still entirely playable, even possibly gigable. If you're willing to play those 50 year old flat frets (I've never seen one with a crown on the frets), you should stick with the stock tuners and bridge.
Luckily, you have the Better of the bridges found on these basses, this one often is found on them
To make things worse, they were often mis-installed on the basses, you can see this one has been moved back so it could be setup properly.
Your pickup is the humbucker of that time that was often in Hofner copies. The Teisco bass offerings were more often regular foil (gold and regular foils pups both used aluminum screen), as you can see on my daughters bass:
The only thing I did on this bass besides new strings and a setup, was to copper sheild it, and it is now the most hum-free Teisco I've ever played. It did darken the tone a bit, but in with this bass... that is a good thing.
You see crazy prices on eBay and Reverb on these things (one recently sold for over $300), but they're not worth it (even to scavenge the pup). You got yours for a proper price.
If you're really going to gig it, the tuner key tabs are the single biggest point of failure, not tuning problems so much, but I've seen many of the tabs just fall off the shaft (over the years).
Enjoy your cheap horse.