I don't have a HT, but I saw a picture. I just installed the Steadyfast on my 30.5 BHLT. From the looks of it, you would have a problem with that spare tire when retracting the landing gear. Not sure when extended though. Although it would be extra work, I suppose in theory you could remove the foot pad then take the entire thing off when retracting the gear. It would certainly be extra work.
To check, extend the gear then use a straight pipe or board from the rear of the footpad to the frame about 4-6" behind the landing gear. If it doesn't interfere with the spare, then that would work. Of course, you could also remove the spare tire and store it on the bumper or something, then not worry about removing the stabilizer's.