As an update to my previous post:
My domains are all now on Name Cheap. It took a bit of time as there was human interaction required in order to unlock the domains and get the EPP codes for the transfer. However in the end all of my domains have transfered over, and I now have the ability to configure DNS for all of them in one easy control panel under one login. I also checked for future shenanigans and to unlock and get the EPP codes on Name Cheap is all done via my account interface.
Here's to hoping that Name Cheap stays how it is for as long as possible, corporate ownership-wise.
I should also note that when I had to deal with people at Westhost duing this process, they were friendly and helpful.