Epoxy putty sounds good. But it needs a backer support. A couple of ideas. Tape over the surrounding paint to keep drips from sticking.

1. can you reach the holes from the seatpost and the headset tube? On the inside of the tube, epoxy in a piece of fiberglass screening or similar. A couple of layers of screening. Apply the putty after this is cured.

2. a thin rod, with a very fine wire or doubled up thread wrapped around the middle. Use a nail with the head cut off? Liquid epoxy on the rod, slide it in the hole endwise, pull it tight against the inside of the tube and secure the wire around a stick until cured.. Oh, and put a couple more drops of epoxy into the hole with the rod in place to wick out along the rod.

It's the same idea as a drywall anchor:



or using a glued in backer for drywall holes: