I have absolutely no problem with putting a puppy away in the crate for a bit when they're wild and out of control. It's like an overtired toddler that doesn't want to go to sleep. I don't see it as punishment, it's just a little downtime, which is important for my sanity! You've given him plenty of exercise and now he needs to learn to settle down and be calm in the house.
It will get better as he matures, but for now, continue doing what you're doing and don't feel bad about it. As you said, he whines for a minute and then takes a nap, so he's obviously not traumatized by being crated when you need a break from puppy craziness. I did it all the time when my dogs were puppies and it's never made them not like their crates. I don't even have to tell them to get in the crate most nights now, as soon as I come into the bedroom at night they run in and lay down on their own, and Keefer will nap in there with the door open if I'm in the bedroom on my Lifecycle.
exactly the same thing only with fur. he isnt being tramatized by crate time so dont worry about it. For sanity's sake he needs it. Shasta would go and go and go and after a few crate sessions she started to chill on her own outside of it. That pup will go until she drops, literally. She'll just skid to a stop, flop down and start snoring a minute later. Dont worry. You're pup sounds perfectly normal.