I finally achieved a major milestone with Eternity II, solving a framed 14x14 puzzle. I had it running on Christine's machine, and it took about 8 hours.
(Here's an online EII you can try, just to see what it is
A framed puzzle is one that uses the EII pieces and is bordered by grey edges, just like the real puzzle. To date, the best solvers have been able to get this, but no one has reported success in anything bigger.
Unfortunately, a 14x14 cannot be used to get a 16x16 solution, but it does give you insight into the larger version.