I have an 84 explorer with ebony fretboard. It's built like a tank. And is a great sounding bass. Mine was painted puke green at one time, it survived the Hollywood hair-metal scene without getting broken... it looks well worn and might have a drug prob. I had a scratchy sound coming from it after a few years of giging and kept looking at the solder joints near the jack which is one of those long throat type inputs. It turns out there was years of built up smeg on the outside of the bas, on input jack ring, making the cord ground not completely. I knock of the junk with a chopstick, plugged in, it sounds perfect. Make no mistake that is a great bass.
You might want to:
Test one pickup then the other, you have V/V/T
check the solder joints see if they have been resoldered,
if they are original they will look clean and molten. If it's been resoldered make sure the pick up wires aren't reversed would give you a thin sound, it should sound big, huge like a thunderbird and mine sounds a bit overdriven (in a very good way)at all volumes, and my pickup are as far away from the strings as I can get them.
To loosen the truss rod, loosen the strings, floppy.
Loosen the truss rod, then tune it up, standard tuning, see if it frets out, also make sure the intonation on the G string is in the right spot, on mine the G saddle is father forward than the E for instance. The distance is shorter, all this matter on how the neck reacts. I play heavy strings too, 50,70 90 110 like all my basses I have to adjust the truss rod alot. My explorer I turn the truss rod all the time since I live in the mojave desert, it's hotter than hell. Don't be afraid to work on your bass, it's built really well. If you loosen the truss rod the neck will for sure make the action higher. Never force the truss rod, you might have to apply a little pressure to get it to turn the first time.
If you can't figure out the wiring let me know I could photograph the inside of mine.