Well I am now officially in the situation I was worried might arise if I started looking for houses before I got converted:

I have found a gem of a house that I absolutely adore, and can't afford it until I get converted. And I have no idea when that will happen. I feel like anyone else in my price range will immediately snap this house up, as it is infinitely better than everything else I looked at.

The bad news is that I asked my deputy group leader today what the status was with my conversion and he said that it had come back from HR for revision. The group leader has been sitting on it for some time now, apparently, because he's "swamped." And now I desperately need to get converted ASAP. The DGL also indicated that it would take "a couple months" once HR took the revised document, which conflicts with the "one week" I had heard earlier. I don't know who to believe, but I have a hard time believing that this house will stay on the market for another two months, especially considering that they dropped the price by $10k this weekend.