What horn is it? Contrabass trombone mouthpieces are -great- in bass trombones and euphoniums for just such a role. I have a Josef Klier KBP2C and a Kanstul (heavy JK copy) 2A; the 2A is just a little too much for my bass trombone but the 2C rocks there and in every euphonium that it'll fit that I've tried. I think it was about 50 bucks from Dillon's.
Think quick (to avoid the "omg!! i have to play a bunch of low notes!!" slowdown) and aggressive (playing loudly enough to bring out the low range) and you'll do fine; imagine yourself to be a bass trombonist with built-in intonation.

Lose the "bwah" and bring the "bah" and make sure you can play low C and B in tune.
I think that if one of the trumpet players could manage an alto trumpet, alto trombone,... for the french horn part that 2 trumpets, whatever horn, a small tenor, and a euphonium could be a very nice sound- very bright and clear. "Trombone players" wig out at the thought of smaller tenors for anything other than big band and, as rarely as possible, the occasional "period correct" gig, but a small bore tenor, with an appropriately sized 5th voice, really blends well with the higher horns. I just saw The United States Army Band brass quintet play and the "small" horn Harry Watters played fit in awesomely with the higher horns.
I think it'd sound even better if you made sure to avoid having a french horn on the third part, but whatever.