Yup, woody voice is the nature of the P pups in comparrison to what your spector does and of course the squires gonna sound lacking compared to those nice humbuckers and preamp equipted spector. You could try putting an active EMG P pup in the squire if you otherwise like it. And the EMG preamp useing stacked bass and treble pot. Alterenately if wanting to stay passive for the P, try Dimazrio or Seymour Duncan P pup. Its gonna take a lot of eq fiddling (I hope you got at least an 8 band eq) and probably some fiddling with gain structures thru processor or amp. Your gonna have to get the squire sounding as comprable to the spector as you can. Not the same as spectors neck favoring pup voice version, but comprable.
Imo 90% or more of in the bedroom practice should be in the mix. With the other sound source playing thru the same speakers or headphones as your bass. Even if this is just with a drum machine. Said drum machine must create a similiar voice to the drums being used by the band. Preferably play along with recordings of the band minus your instrument. Or at least with drum machine and the other main soundbed instrument of the band. Or with recording of other bands who have similair sound to yours.
Ones primary voice should be one crafted to sound good in the mix. If your guitar players wont adjust their sound to sound good in the mix. They either need replacing (best option) or the rest of the band must modify their voices to sound good in the mix with the guitar players. Better yet, take away the guitars players rigs. Have them play thru their fave processor set for ready for recording tone. This signal is then sent to Pa with some nice person doing whatever must be done to make guitars ound good thru Pa in the Mix. Lol. If more guitar players spent more time playing along with mp3's thru headphones, theyd have better in the mix voices. Same goes for bass players too. Lol,
Thats how you get sounds good in the mix voicing. By tweaking your voice in the mix and only in the mix. Sometimes the main tweak is adding more overdrive. Compared to the sounds wonderful solo voice which sounds weak in the mix.
Those who craft their instruments voice solo should not play in bands. O ok, so everyone does that some. But untill a peepp learns to tweak their voice in the mix to sound good in the mix, its never going to be as good as it can be in the mix. If nothing else, use cd;s or mp3's of similiar sounding bands as the background in the mix source for coming up with your ready for recording voice.
That all done, you can start tryhing the instument out with the band spending time initially getting it to sound good with the drums, then the next main instrument added in. Etc. Getting input from the rest of the band about how your isntrument is sounding. If more bands did this cooperative in the mix best voices creating. Theyd not only sound better, theyd make better music together. Imo.