I think I'm explaining it badly.
The GPS module (EM410) works just fine. I can connect it directly to the UART pins on a Raspberry Pi, start the gpsd service, and everything works.
I wanted to try to isolate it from the RPi to see if I could reduce the noise reaching the GPS receiver, so I got the bluetooth serial module (HC-06). I expected it to work something like a "wireless serial cable," but it's not so straightforward.
The GPS module connects to the bluetooth serial module. I connect wirelessly to the bluetooth module with the builtin bluetooth adapter on the RPi board. So on the RPi, the configured link shows up as a the serial device "/dev/rfcomm0". Using stty, I can set the speed of /dev/rfcomm0, but the remote bluetooth module will still be running at its preset baud rate (in this case 9600bps). Since I can't set the wireless link to 4800, I can't make the initial connection to the GPS module.
Now, I can take everything apart, physically connect to the bluetooth module, and tell it to communicate at 4800bps. When I put everything back together, I can then stty the serial device to 4800 and speak to the GPS module.
But then I'll be stuck at 4800bps forever.
Again, the cheapo GPS modules work great with gpsd already. I'm getting a little too ambitious with them...