So I called my new AME's office today to inquire whether he will be doing BasicMed exams. The front desk person sounded at first as if she had never heard of BasicMed, and asked me to explain my question. Once I'd done that, though, she said they were "very familiar" with it, and yes, he will be doing the exams. Earliest they could fit me in, though, is May 12.
That's a little better than the 18th though, which is the soonest my PCP could fit me in. Given my PCP may not have the equipment to do everything required (in particular, color vision testing), I'd rather go to the AME anyway.
Just a couple more weeks, give or take...