This is going to sound like I'm being a deliberate d-bag, but it's not intentional.
I was wondering if you could delineate what "limitations" of your "cheapies" are and what your "pros" have that are lacking in the others?
I mean, a Squier or Epiphone (or SX, etc.) may always be just that, regardless of what you do to mod or upgrade them, but it's been my experience that a cheapie can be made perfectly giggable and playable even if you might spend a little cash to get there with regards to pups/electronics, hardware, setup, etc.
My "best" bass at the moment (though I've sure owned a slew of more expensive and "nicer" ones) cost me $320. Actually, I got a HSC priced at $130 thrown into the deal, so essentially the bass was $190. Cheap.
I bought $16 chrome knobs for it, a $25 pickguard and $4 cream pickup covers. All cosmetic.
I did buy a used replacement pickup ($55) and a new premium wiring harness and jack ($30) because as decent as it was, I thought it could sound better and I like messing with stuff.
Bridge and tuners are fine and fully functional. I don't feel the need to replace them.
So, cosmetic mods aside, I'm basically into this one for $275 and I think most people playing it, if they knew their stuff, would say it's a darn nice bass.