HI Bill!

That would need completely new design of TRXcontrol. Maybe a database for rig (and keyer) settings that would then be called from rig selection combo box.
Not impossible, but needs lot of work.

As a workaround I have suggestion:
Set cqrlog radio settings to use model #2 NetHamlib Rigctld. Uncheck "Run rigctld at program start". You can also clear all other settings except port, poll rate and host.

Then do three command line script files to use with your 3 rigs.
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#!/bin/bash
killall rigctld
killall rigctld # this line is not needed but will make sure that all previeus rigctlds are killed if there is another lying down somewhere
/usr/bin/rigctld -m 3073 -r /dev/icom7300 -t 4532 -s 19200 -C auto_power_on=0 &
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Use parameters your rigs need and do not forget " &" (space&) from the end. That makes rigctld run on background.
You can make desktop icons for all these for easy access.

When cqrlog is running execute one of scrips. After that switch TRXControl radio1/radio2/radio1 or use NewQSO/File/Refresh TRX/ROT control to make cqrlog reconnect to running rigctld. You should now see that TRXControl works with scripted rig.

When you want to switch rigs again, to the same but with different script.

That works but you can have keyer definitions only for two radios (TRXControl radio1 and radio2) and also user defined buttons (latest cqrlog versions) can support only 2 sets of definitions. But they work with 10^n rigs if same commands are ok for all those rigs. (you can even define 3 script starts to these 3 buttons!)

If you use wsjtx, jtdx, js8call, qsstv, fldigi with cqrlog use rig model #2 also with them to get them work with same rig as cqrlog. At least wsjtx/js8call will complain when you switch rigs but will reconnect with retry button. I have no experience what happens with fldigi,qsstv and jtdx but restarting the rig connection somehow connects them to switched rig again.

Maybe not user friendly, but working workaround. And the amount of rigs (scripts) is unlimited.