Ah, there have been a number of threads on this over the years. I'd do a search in this forum and you'll come up wiht a lot of helpful tips.
A few ideas, not necessarily in order of preference:
You may have to reframe your take on "gifted kids needing less sleep". It's myth, has been debunked by science. Some gifted kids need less. Some need more. they're all over the place, like typically developin gkids. What they DO have in common, most of them, is trouble with winding down and falling and staying asleep. The "overdrive" you notice during the day may be due to lack of good quality sleep, even.
I would not focus on wearing him out physically. I would focus on his sensory diet instead (google that one) and his "nature diet" - don't google that one, I made it up, basically try to do your exercise outside in a natural setting whenever possible. Again, don't focus on the wearing out part, but on the richness of the sensory experience. Physical exhaustion actually makes it harder for my kids to wind down. And keep the social stimulation down: running around with other preschoolers in a gym may make the situation worse. A hike in the woods behind your house (hope you have them!), getting real wet and muddy, having a hot bath afterwards, may help. Then a back rub and a book.
Mental stimulation, yes, but watch out for overstimulation. It is so easy for these kids to go into mental overdrive, too. We have found, for instance, that making our DS1 lie still and listen to gentle fiction at bedtime worked better than reading a nonfiction book and having him excitedly take part and discuss the contents. So more exciting things during the day, slower things at night. NO screens after dinner. Low lights, the parent reads, the kid snuggles in the dim corner.
Check out low-carb high fat moderate protein diets (primal/paleo). Made my kids sleep better and made us sleep better, too! Regulating insulin production is a huge need in our house, for all of us we've found. NO carbs in the morning, no sugary snacks, no soft drinks. No we don't always manage but we try.
Fish oil, zinc, magnesium. Specifically magnesium (start with 200mg, preferably citrate, lower dose if it causes loose stools) has been a wonder drug in our house. Some people in this forum have had great results with melatonin, both slow release and regular.