i don't do seeds in hydro, for the same reason as you're having probs with. rockwool starter cubes work well, as the whole plug can be put in a net pot.
the less you disturb the root structure of the plants in hydro, the better and faster they will grow. i root clones directly in a net pot, so there is no transition. i have also rooted clones in an aerocloner, and transplanted to net pots which works well. coil the roots on some medium and fill in; roots take about 5 days to grow out of the pots.
i'd say your best bet for getting small plants from one spot to another would be rock wool. just be careful you don't keep your cubes too wet, or the seedlings will rot off at the base.
kp