@Salectric, heard back from Millersound - they do not have parts and thus do not feel confident they could maintain their high standards while working on these speakers. That denial is a true sign of quality work in my book. They did, however, recommend I reach out to Jonathan Weiss of OMA, which I did.
Jonathan has been of great service to me in the past year as I've tracked down old RCA gear. He had helped me work through the different parts of an old Photophone theater system I picked up last August.
I placed a call to the number listed on OMA's website and was surprised when Jonathan picked up. He was kind enough to talk about RCA and not his own business - in his words, with a broken LC-1A it's best to just walk away. Repair parts for a blown tweeter don't exist; he asked for an update if I did find anything out about possible repairs, otherwise he said it's best left as a parts unit.
I've got these boxed up for the time being while I continue the search for repairs. Art Dudley's writeup on the speaker made it seem like parts could exist somewhere - I wonder if it's possible to reach out to him.