I also have the MXZs, and they are awesome. I wear one pair of ski-socks underneath. When the temps dip well below freezing, and I'm going to be out in the cold for many hours, I also use chemical toe warmers.
I wonder if you're not cutting off circulation by using two pair of socks? That would account for the cold. However, sweat could also cause your feet to get cold. I'd try the ride sans the Nashbar wet-weather socks. They may be too clamy for your set-up. The Lakes are pretty much water-proof, so you really don't need that type of sock underneath.
Good luck, and please let the group know what you find out.
Most of the I wear my lightweight summer time Sock Guy wool socks with my MXZ 300s. The MXZs have enough insulation that I don't need winter time socks. On a two hour ride at 15 F, my feet will be fine. Colder than that, or longer than that, and I'lll consider thicker socks.