I recently upgraded my Electra Phoenix x630NA (1983, without pickguard) with another Delano bridge pickup, the SBC 4 HE/S (it already had the Delano PC 4 AL pickup.) Yes, had to have it routed. Two 500k volume pots, one of them push/pull for series/parallel, no tone. (Best thing with cheapies is that they rarely have huge resale value, so they are good for experiments!)
Incredible, refined, P bass sound, a blend of modern and old, without losing the P bass vibe at all. Basically, P bass sound+++ (note that I do love the "normal" Fender P bass sound, and I am not demeaning it in any way or fashion.) Sounds like a high quality P bass recording, even without equing. No noise at all either (of course.)
The Delano vintage pickup was already clear, and with the addition of the bridge SBC 4 HE/S, it's super defined, no mud anywhere, not even in series, it's just a beautiful sounding "cheapie" bass. I am amazed at the natural sounding Delano pickups. Both the P and the soapbar pickups blend beautifully. It's not the sound of a P/J (which I didn't want) but it WORKS incredibly for me and my specific playing needs.
Have to add that the seemingly simple Electra x630 body is incredibly easy to play with a "jazzy" neck, and the horns are comfortably placed, so everything plays fast on ALL frets.
Why part with that which works?

If anything, if you love your cheapie, treat it with love and upgrade it as needed. Make it your own, customize it, make it sound the best it possibly can.
(Have to add that without Brian Ristola (bestbassgear.com) the succesful experiment above wouldn't have ever happened. His recommendations, according to what I was asking and what I told him I was looking for, were spot on! My props to Brian and everybody at bestbassgear.com)