Squirt,
In your position, I think I would let him read and do Aleks over the summer and then start 3rd at the private school in the fall.
The retired GT teacher doesn't know Pud. The school that tested him thinks he should skip. Pud wants to skip. Those are huge arguments in favor of skipping which are not negated by the GT teacher's opinion. You already tried letting the teacher challenge him. Didn't work. If your school's gifted program is like ours, don't hold your breath hoping for challenge there.
I understand your feelings of trepidation--just look back a few months to see how I wrestled with DS' skip. The skip has worked beautifully for DS so far. I'm sure it's not a permanent solution, but it's good for now.
Cathy