Small, embedded, stripped screw heads are the worst to remove. For any non-stripped heads, you want to use a blunted Philips #0 screwdriver to remove (file / sand down tip to properly remove).

I don't have a great way to remove these screws without potential damage.

Some people drill out the screw head but then you're still left with the shank embedded into the screw hole.

The epoxy method is very risky and may not even withstand turning forces. You basically stick a screwdriver head and screw together. Then you try to unscrew the screw. This is risky as it would be difficult to prevent the epoxy from getting stuck on the sides of the plastic hole.

If you're very skilled with a dremel and using (sub)millimeter drill bits, you could try to carefully drill a slot to fit in a flat head screwdriver. Have to be careful and not damage surrounding plastic or drill through the screwhead and damage plastic underneath.

There are specialty drill bits to remove screws but those are too big for typical toy screws.

Good luck.