By my count there are 52 goalies available. We, as a league, will need to draft a minimum 48 of them.
25 of the 52 played at least 50% of their games.
So if you play this out, the question in this particular draft becomes, when do you take your goalies? I could see a goalie run happening in the third round.
At some point you'll have to decide whether to skip that 4th defenceman and take your 2nd goalie. Much like any draft I've ever been in.
You say you're worried about some team getting royally screwed over in net, well to further what chuckinrlp said, if that happens to you it's your own damn fault. Then you'll just have to take that 4th defenceman you held out for, and trade him to someone else who cornered the goalie you didn't.