I think your son will be fine. I have no idea what "doublespeed" 7/8 math would be - is that school lingo for Pre-Algebra? Accelerated math in most districts near here is Pre-Algebra in 6th, Algebra I in 7th, so I think that kids like your son would do just fine in Algebra I.
Doublespeed is a word I made up because Accelerated Grade 7 Math is grade 7 and 8 math in one year. It's the start of the Honors track. The school says it's "breakneck paced". Makes me nervous. They're probably used to parents and kids who freak out.
I heard somewhere that things learned quickly are forgotten quickly. Things learned slowly are retained. I suppose this theory does not really apply to most gifted children? 8th grade fill-in-the-gap summer study is reasonable?