Megmeg,I fully understand. Stubborn, strong willed, intense, all describe my ds5 perfectly. And just yesterday, we went through the same battle. I said, no playing until 20 min of school work was done. 5 hours later, and much whining, he finally did it. Luckily, we home school, so he doesn't even know what spring break is. But I have been requiring 30-60 min of school daily (4 times a week) since January. I often too feel conflicted, knowing he is working about 4 grade levels ahead...but I also realize, that he has never ever had to do anything structured. While most kids his age have been in pre-school, he just played...so now is the time to gently learn that work comes first, and that he needs to do what his mom/teacher ask. I know if he doesn't learn this now, it will be harder down the road. But I too feel intense conflict when I have to push so hard. But I know I need to win more battles--he wins too many by being so good at arguing, and having tantrums. So yesterday, I knew I was in for it, but went ahead, because he promised me to do his school while we are away from home for over a month. But not every battle is worth fighting, but once you've put your foot down, you need to follow through.
I too, plan to continue schooling over summer--30-60 min a day, and while others look oddly at me for that, I just remember, that their children have already spent more time in structured situations than mine, by far. And I am just trying to keep a structured training going...An hour a day is hardly something to call infringing on free play time.

If your child needs to continue with a little structure just to keep the routine going, you are the best judge of that. I wouldn't do the battle daily, but if you have to battle though a few days, just to let them know you are the parent, fine.

Strong willed kids are a battle, and as much as they do need more autonomy.. I think they also need to be reminded that they are not always in charge...I KNOW my DS needs that reminder. 30 min a day is not too much...it is no different than the school asking to read a book over break...it can easily be worked into the it is just how we relax catagory..with a good book and a couple of brain teasers.
Good luck! And don't forget to bring the Play on once the battle is done!