Sorry to drop in out of the blue. I'm V20 partner involved in firm recruiting. I've lurked off and on for a while; with employer roundtables and interviews on the horizon I've been catching up. I'm writing on a phone watching NBA playoffs; pardon the many typos and grammar issues I'm bound to make. I'm observing and providing some insight. Not answering questions. Hope you'll forgive me that.
First, an observation: prospective students have much more information now and are assessing options in a more thoughtful and methodical way than I could have 13 years ago. That's great. (Though polling strangers that don't have the same options or information as you has marginal value except as entertainment.).
Some key misconceptions/uncertainties prevail in the discussion here. I'll try to be thread-specific. I'm only addressing big firm behavior here and I'm basing this on personal experience plus discussions with partners at other firms.
First, let me confirm that each top firm (at least in the markets where I mostly practice - NY, DC, Chi, Bos) essentially saves summer spots for kids from each of Y-Chi. (NYU is a bit different in a couple of markets for historical reasons. UM or UVA get spots held for Chi and DC, for example. NYU is golden in NY and the grads tend to stay there, so not much thought is given to it in some other markets, relatively speaking, IME. Cal is a similar example.
(The flip side of this point is that, yes, T6 (with minor variations at the "bottom") is real. Be very careful with the common wisdom I see here that "after HYS T14 is mostly the same". For the tippy-top firms, that's just not true.)
So, as a law student you are not competing with other schools so much as your classmates. Once an SA and then an associate, you are generally judged on your individual merits and you compete with your peers at the firm.)
While a top firm (or USAO or judge) might be go "deeper" into Yale's class than UofC's, now would seem to be an odd time for the OP to bet against himself and pay a lot of money for that cushion just in case he doesn't do splendidly his first year at Chi (or Harvard or Colombia for that matter).
Also, since the very most OP can make as a first year is capped at 160k plus bonuses, I don't understand arguments about the marginal extra earning value of the Y degree. OP has little reason to think he won't be at least mediocre at a non-Y T6, which is in fact all he needs to get in the game at a big firm. Not getting a good job in 2014 from a T6 is a remote and I'd say unlikely risk. The debt, a risk in its own right, is real and much more certain.
Finally, anyone who thinks there's more "prestige" in the name Yale than in Hamilton or Rubenstein is nuts. People get into Yale (and Stanford) for all sorts of quirky and good reasons. But the top full ride T6 scholarships are rare and signify top credentials.