I'd check the child thing with the manufacturer, or a manufacturer of a similar rig.

I can't really see the point of brazing on the eyelets. By the time you have bought all the stuff and wreaked a few tubes, and burned off all the paint, it isn't going to look that slick. Seems like a lot of money for the bike that is probably attached to the drop.

It's not so difficult to do a braze-on, it's just the kind of thing that has a high up-front cost, and will take a few tries to get right. So practice on something burnable for starters.

I would try some superior mechanical solution, like something built around the cuttout in the drop, a u-bolt, or a piece that bolt and clamps on like clamp on deraileur mounts. I'd also go for the P-clamp. Not so long ago that was the standard attachment for a rack, even on a touring bike.