> There is no force acting on it to bring it back down.

Gravity?

But also orbital dynamics (at least as I understand it) means debris that debris that is flung up is going to have a more oval orbit, so the high point (apogee) increases and the low point (perigee) decreases. And a lower perigee means more atmospheric drag, which will help deorbit the debris.

>means debris that debris that is flung up is going to have a more oval orbit, so the high point (apogee) increases and the low point (perigee) decreases. And a lower perigee means more atmospheric drag, which will help deorbit the debris.

Not quite.

If you are at apogee and accelerate, your perigee will be raised. If you are at perigee and accelerate, your apogee will be raised. You can't increase your apogee and perigee at the same time.

If the impulse is in the direction of orbit, then the altitude of your orbit 180 degrees from your current position will raise. If the impulse is against your orbital direction, your height 180 deg away will be lowered. Once you complete an entire orbit (360 degrees) you will pass through your current position again.

If you wish to move to a higher, circular orbit two impulses are required, 180 deg apart.

That'd have to be one slow explosion to give it less than 1G of acceleration.