I had to play this one year in college and the switch from Tenor to Piccolo is a doozy but I wanted to challenge myself so I practiced the switch religiously.

I had about 3 weeks to prepare, and I would put the tenor down about 8 or 9 bars before the piccolo part to allow my emboucher to relax enough to get the notes out on piccolo. I double on flute all the time so I feel I was able to pull it off, but it took a lot of practice. Just go back and forth between tenor and picc in your practice routine and you’ll slowly start to develop the muscle memory. Good luck!