Hey weekapaugh,
I have had a Tribute for nearly a year and I am still discovering new tones. I can't say enough good things about this electronics package and the breathtakingly beautiful, super sweet sounding guitar Alembic made for me. I have largely let my effects gather dust so varied is the palette these guitars give you. However I have at times used a phaser, octave divider, overdrive and delay pedals with no problems whatsoever. I did have some issues with a rather old beat up Mutron III, but they disappeared when I accidentally dropped the Mutron on a hard floor, so there you go... For the use of effects I really like the on-board loop in the Tribute electronics. It is very convenient and having the loop wired pre-volume lets you to some extent set and forget when you adjust volume and if you want to have the loop post volume I understand that is a simple tweak you can do yourself.
I have always quite liked Phish, but am not super familiar with all their tunes, however after seeing your post I put some LivePhish discs on and tried to play along a bit. I understand Trey's guitar is a vented hollow body with two humbuckers, is that right? So the Tribute is going be sort of a horse of a different color, but I did find I could get what I thought sounded like pretty Trey-like tones.
Discovering stuff like this is half the fun (thanks for making me think of it) so I won't tell how I did it. Just start with the neck pick up on, middle pickup on bright, bridge off, tone filters slightly rolled off and start experimenting from there. You won't be disappointed.
All that said I don't have the greatest ear and its kinda subjective, so if you are near Alembic stop on by or visit on of there dealers that haev a Tribute or Further in stock and check it out. It worth the trip! Wow thinking this through, I am all psyched up to go play now.
Enjoy,
Court