Er, why not just a Friday at 11 PM EST? It's when the 1-on-1's show up, so people who don't know about this will probably be logging on anyway. It also works OK for people on the other side of the world. Not too great for UK I understand, but eh, it can't be perfect.
Or we could do a Saturday 7:30 PM EST/11:00 PM EST/11:30 PM EST.
This Friday is the 2nd EST, and Saturday is the 3rd EST.