Noah,
As you know, I play two horns, one with trigger and one without. This is by design since I wanted the Adams optimized for light weight and ergonomics while I also wanted to keep my heavier Sterling optimized for its sound and playability. Based on my experience, I want to put a +1 to what Dave said about the approach to using the euphonium trigger to adjust pitch the way one does on trombone. Sage advice!
Also, I am not big fan of "added on" triggers. The engineering to get it "right" is not insignificant. Changes to bracing on the 3rd valve slide and main tuning slide are generally required to provide stiffness and yet room for the trigger to operate. The linkage needs to be well engineered to allow easy tuning adjustment, positive up and down stops, and yet also permit easy tuning slide removal for cleaning. The tuning slide itself needs to be carefully aligned with the legs and everything needs to be straight and parallel, just as on your trombone. The fit between slide and legs needs to be loosened just the right amount so air seal is good, but friction is dramatically lessened using an oil or trombone cream. Finally, the need for an adequate "guard" or belly pan to keep the slide from hitting your body without causing all of the weight to be carried on your arms is often overlooked on the add-ons.
Mr. Ruby
Adams E3 0.60 Sterling bell - Prototype top sprung valves
Concord Band
Winchendon Winds
Townsend Military Band