Hmmm... I thought I was a square peg in a round hole when I installed the Trig TC20 control head rather than controlling the TT22 from either the HX or Mini-X. My thinking, and it was only thinking since I still haven't flown behind this instrument panel, closely mirrored yours, Bob. Thanks for confirming the aspects of EFIS-related workload associated with remote transponder operation.
An added benefit of installing the TC20 control head is that it is also a TSO'd altitude encoder for the TT22 transponder. Some avionics shops give grief when using an EFIS as the encoder source - the TC20 takes that argument off the table. The "reported Flight Level" readout on the TC20 display is a nice feature that allows one to always see the altitude being broadcast, and can even, in a pinch, work as a 100 foot Pressure Altitude altimeter should one's primary altimeter fail. Just remember it's in 100 foot increments, and it's altitude relative to 29.92" pressure setting.