That's beautiful! Congratulations! I wondered throughout this entire thread if there was a way to do some creative hack or abuse of the protocol to get the needed effect, but I never knew enough about TLS to come up with one.
The only issue I see, which I'm sure you already thought about, is that by stripping the server MAC it may become possible to do some kind of content injection MITM attack on the live connection. However, as you can snapshot just a single page and the user already knows what content to expect anyway, I suspect that's not a big deal in practice especially if the HTML is not rendered (as otherwise various kinds of cookie stealing attack might be possible). I mean, I suspect it's rather hard to usefully inject data into the middle of a TLS stream even without the server MAC, but it's obviously there for a reason.
Is there a risk of k-lining or attacks if using IRC for rendezvous? IRC is typically unauthenticated. I wonder if direct ip to ip with STUN would be feasible.
edit: By the way, I'd suggest running your scheme past Adam Langley and see what he thinks. He is a TLS expert who works for Google and has designed a bunch of recent TLS extensions.