They dont eat for the first couple of days, so daphnia is all i would suggest to leave in the tanks (is it will not die like bbs). Personally I think a net is fine to remove the babies, My axies had eggs in a 3ft tank the other week and i removed the parents an let the eggs hatch in approx 30-50cm. then after the first hatcher i removed eggs on a daily routine into small lunch containers approx depth is about 2-3 times the axies overall length or a bit more, and placed in some daphnia.
Dnt worry about them not moving alot, they will generally only move for a feed and air bubbles in their belly making them feel uncomfortable(if there well fed and have an air stone you shouldn't have this problem). So stillness is good.
Hope I have been helpfull