Jim,
There is a similar but not identical issue with my FT-847. I have used two different approaches.
I used to run the leads, mostly in parallel except for the 1200 and 9600 baud outputs, to radio ports 1 and 2 on the DSP-2232. Switching the modem loaded automatically switched the inputs and outputs.
Since I started using sound card programs several years ago, I made up a simple ABC switch. DIN cables, jacks, boxes, and wafer switches are cheap at a good hamfest, and not that expensive at parts stores. Another trick for a selector, which I saw documented in QST, is to use a serial AB or ABED box which are cheap, and nearly free at a hamfest flea market. You can make up adapters, or install DIN sockets. All the wiring is at audio frequencies and is uncritical. A metal box for shielding is recommended!
Note that however you do it, the audio levels from the DSP-2232 are not constant when you change the modems. If you use the same radio port, you will need to provide some sort of means of equalization. I used some cheap trim pots in my switching box. If you use separate radio ports, you can set them individually using the DSP-2232 level controls.
Alan WA4SCA