Tight budget, no experience installing a tremolo bar.

Need advice: shop for a pre-installed bass whammy, or suck it up and learn how to install one myself?

Also considered spacing out the strings on a six-string guitar (w/whammy) so there’s just three. Any hope for that?

Kindly,
Apoxode

You mean putting something like a Bigsby on a bass? I do not think this is something that would work well, because the enormous tension of strings on a bass might be too much for it to structurally hold together for long.

You’d probably want to get a bass specifically designed for this like the Squier/Fender Bass VI, which uses a lighter gage of special strings that aren’t as demanding on the bridge. The Bass VI has a tremolo built into it, so you would not have to mod it either.

https://www.fender.com/en-US/squier-electric-basses/other/classic-vibe-bass-vi/0374580506.html