After a little more experimenting, I have to chime in and say that
@DiabolusInMusic and
@jive1, have probably hit the nail on the head.
I spent some solo time at our rehearsal space last weekend and again last night. I turned the tweeter off and plugged his P-bass, intent to prove myself right. It sounded "better" with the tweeter cut, but still not "great." There was still a noticeable amount of trebly click clacking happening. I tested the tweeter at various levels and, to be honest, it really didn't make an enormous difference unless turned up to -2db or so. He typically keeps it on -4.
I brought my SG bass in last night and plugged it in, just out of curiosity. Sounded amazing. Deep and full and punchy, great spectrum of frequencies without the harsh high end noise and clacky stuff. And get this -- I even found that I almost LIKED a bit of the horn mixed in, albeit a bit lower at about -6db. With just the bridge pickup and some nice pick attack it was grinding away right on the edge of overdrive. With the neck pickup mixed in the big fat bottom end just kind of blossoms out into the room and blows you away.
So it's not the amp; and it's not the cabinet; it's not his technique (my playing is very different form his, but with his P I still get the clack); so i guess it's the setup. Which actually makes it a harder thing to tackle, unfortunately. He has a variety of basses and I've noticed the clackiness on each of them. I'm not very experienced with bass setups so I don't really know what the cause is. The action doesn't feel absurdly low, but it's definitely lower than I play.
At any rate, I feel much less comfy asking him to adjust his setup, which seems like more of a personal choice. This band is just for fun, not making any money or even trying to -- so I'll just have to learn to deal. Have to say though, I just don't get the appeal of that sound.