For those curious how this went:

I replaced Q17 and C54.

I now have correct voltages on all four pins of the PA module in
transmit mode, but still almost no power output -- I suspect a bad PA
module, at this point. Reinforcing this is the fact that I appear to
have more signal on the input of the PA module than I have on the
output.

I think I'm going to set this one aside and just use it as a receiver;
at this point it's not worth spending much more time on, unless I run
across another IC-28A with a different problem.