In short: at what point could a floor majority ram through an organizing resolution? Is there any such point? What's the longest it's ever taken to get the resolution approved?
I think the issue is that the organizing resolution, like almost everything else in the Senate (except, I believe, conference reports), is subject to filibuster. That means either the Republicans need to get 60 votes (to override a filibuster) or do it by unanimous consent.
My guess is that they only have 52–54 votes for whatever they want to do at the moment; the Dems are holding out for basically the sweetheart deal they got from Lott in 2000 (which they promptly reneged on when Jeffords defected). They may also be tied up over a few other things — like judicial nominations.
So that's why (a) this is taking so long and (b) you'll never see a provision that forbids a change in control of the chamber due to a defection until one party has a wide enough margin. (However, if any party does ever get a 60-vote majority again, which I don't see anytime soon, you'll probably see a permanent rules change that either stops the chamber from being reorganized mid-session or forbids filibusters of organizing resolutions.)
The irony here is that Senate committees are relatively powerless; you can amend to your heart's content on the floor (unlike in the House), so they really only function as gatekeepers due to mandatory referral of legislation. (Hence why I made fun of Trent Lott's new job a few days ago — one he won't have until the organizing resolution is approved.)
I don't know the answer to the last of Jacob's questions; Senate control has gone over a few times in the past fifty years or so, but until the 1980s partisanship in the Senate wasn't very intense. I've certainly never heard of it being a problem in the past.
Two additional points: as far as I can tell, the organizing resolution has historically been adopted by unanimous consent (which suggests it is subject to a filbuster), and there was protracted wrangling over the OR when Jeffords defected in 2001.