I think the contract for a drafted player should not become effective until their first training camp.

For example:

I draft a player at 1.10 and trade him for the player drafted at 1.12, plus another pick (this is all done during the draft).

Currently both teams would have to eat the signing bonus for both drafted players.

In actuality this is more like the real life equivalent of trading the "draft rights" for that player, since they would not have signed a contract while the draft is still going on.