Looks fantastic as always.

It's doubtful that better pots will improve the volume, though you may have a high resistance solder joint which is taking the edge off the output. The pots I fitted to my ES-3 kit suffer from all the action being in the 8-10 range, and these are Bare Knuckles custom CTS 550k vintage taper pots! Back to standard CTS 450 series audio taper pots for me.

Are the strings the same type as on the P-bass? A thicker string will give slightly more output, and some string materials give more output than others. Though your pickup height looks to be fine from the photo, if the P-bass pickups are nearer the strings, then again that will give that bit more volume. And the pickups themselves may have different outputs with different numbers of winds. 50's style PB pickups were wound a bit hotter than 60s style PB pickups. The DCR of the TR pickup at 10.6k is on a par with Bare Knuckle's 1965 style pickup, which is about 1k less than the BK 1958 style pickup. I'd be more concerned about tone than about a slight volume difference, as you can always turn the amp up but you can't change the fundamental tone of the bass. You can adjust it a bit with the amp's tone controls, but the bass's tone will still come through. So if you are happy with how it sounds, then I wouldn't worry too much.

I'd also suggest that string-through is more likely to affect the sustain and tone than the primary output volume.