codeml in PAML, but you'll need to generate many input files and loop across them. A lot of CPUs or a cluster will be your friend here. I use it for exome-scale datasets.

HyPhy can be a bit of a pain to use due to poor documentation, but you may be able to speed up your analyses using FUBAR.

Hope this helps. I'd appreciate other suggestions, too, if you stumble upon any that are at least as sophisticated as codeml.

Edit: this popped up in my open list, and I didn't see that it was quite a few weeks old. Didn't mean to necro but hope it helps nevertheless.