Thank you Artifice. So waits, take out the T for the message, then add the T from fat.
My ill-expressed question at 35 was really about the wordplay of 21a but it applies to this one too. Did you and xwordfan manage to work out the wordplay going forward, or did you guess the answer and reverse engineer?
I have a theory that some wordplay is so cryptic as to be insoluble without sharing the setter's advantage of seeing the answer. (But I also have a fear that all wordplay is soluble ... if the solver is clever enough!)