Barring creative chemistry, you can dig them out or simply mow them down (I'm not sure how mowable your incline is) and keep mowing them down if they re-sprout. Which they probably won't, but with hundreds somebody's going to manage.

If limited creative chemistry is OK, put on latex gloves. Wet a sponge in Round Up and go swipe the sponge on the maple leaves. You'll use a minimal amount and still kill the tree (we tend to over-use the stuff, it really only takes enough to make the leaf shiny).

With that small an amount, you will need to hit every leaf on the tree to assure that enough gets absorbed to kill it. And a few will survive and need to be done a second time.

The best solution is to mow them, and keep them mowed.

In the first year you can keep the cut off with a string trimmer if they are in places you where you can not get your lawn mower.

It that have grown beyond a sting trimmer, then a brush blade on your sting trimmer will take care of the problem.

I have found that maple seedling usually die after being cut off once and do not come back.

NOTE: I have used the maple seeds to mulch the flower beds with minimal problems of maple seedlings coming up.