Implementing Quiet Time that's actually restful

[MadameFancyPants]

DS is almost 2 and is refusing to nap.  It's been going on for over a week at home but yesterday his teacher said instead of napping he chose to run around the classroom shrieking (in a playful manner) which disturbed the other sleeping classmates.  FWIW he goes to school two days a week.

At home we've been doing our nap routine but as soon as I leave his room he's up playing and just all out destroying his room.  If I delay "naptime" he gets over tired and then it's really bad.  I'm fine with him playing alone in his room, but it seems like one of three things occur:

A) Plays then climbs in bed and naps

B) Get hurt then is even more cranky and still won't sleep

C) After an hour or so of playing he lets me know he's ready to move on to the next thing.  He'll be chipper for another hour or two then MAJOR meltdowns happen.  Still no sleep.

I'm worried that he's going to continue to be disruptive at school if I can't help him learn that he doesn't have to sleep but he needs to be quiet and calm while resting. 

WWYD?

[Megan73]

This may not be popular but here goes...
DS - age three - has just started doing this and has put himself in some dangerous situations - like climbing atop his dresser and chewing paint (!!!) off (thankfully lead-free) wooden blinds.
We told him that it's up to him whether he sleeps or not but if he can't stay in his bed during quiet time then the natural consequence is that we'll turn his toddler bed back into a crib. It seems to be working. He's allowed to bring his menagerie of stuffed animals and some books into his bed.
If that's too abstract for a two-year-old, you could just put him in a crib or playpen. My DS slept happily in a crib - refusing a toddler bed! - until his third birthday. Obviously this won't work if your little one is a climber.