Jeremy,
I am sorry that I didn't see this thread earlier, thanks for the PM.
Yes I agree with you on the first coral that it is anthocercis.
The second is a bit tougher. But I am inclined to A. willisae as it has a highly fused base and the very short branclets with a roseate pattern to the corallites.
I hope this helps. These are some rare specimens so I hope the do well for you in the long run.
Chris @ RM