Thanks for your help, folks.
Went through the application source code (written in DBL – DEC's Dibol variant) yesterday to see if there might be a stranded command that changes the COM port settings. Didn't find any. The only place it talks to the COM port is where it opens a channel to COM1, dumps the data into it, and closes the channel. It does it repeatedly most of the time without “misfiring.” Just to be sure, I reissued the MODE command just before opening that channel. No change.
Also spoke with the Black Box people. They say their converter simply takes the 8 data bits from the COM port, reassembles them into a parallel stream, and sends the stream down to the Centronics plug. The DIP switches on this adapter are set to the same values as the COM port. They also suggested I bring the speed up, so I set it 19200, the max under DOS 5.0. Other than that, they say their converter listens to the printer for send/stop signals. The data streams are short - less than 1Kb total, way below the printer's 14K buffer capacity - so a stop signal is presumably never issued.
Further digging revealed that some escape sequences are not passed, the wrong sequence is passed, or are somehow packaged differently. This printer uses the Epson LQ-860 command set. However, symbol set “ESC (s12H” (27,'(s12H') embedded in the application software - and called under certain conditions - for example, locks up the printer whereas its decimal equivalent, 27,77, seems to get through OK. The lockup remains even after an initialize (27,64) string is issued. Don't know what effect other escape sequences might have.
So it seems the problem is not with the COM port setting after all. In any case, printer control beyond issuing basic commands is not my forte so, to eliminate the converter as the source, I ordered a serial interface, KX-PS14, for the printer. I'll see how that works and report back.