Would it be sacrilegious if it did SSB? 

In fact there is at least one variation on the PRC-64/Delco 5300 theme that IS SSB.   A fellow who works for Delco in Kokomo found it in an archive storage vault and was able to rescue it -  Delco 3200 s/n 1.    I've talked to it on the air and it seemed to work fine but obviously didn't have much of a future.   Unknown if any others exist.

73, Bob W9RAN