Bill,
I don't have a 200S, so my thoughts may be of little value. But I looked at the Sig 200S install guide, and am staying at a Holiday Inn Express tonight

...so here goes:
I have a D100/AP-74 and a 396 fed to a GMA-340 audio panel. I know yours is not an audio panel, but one lesson-learned may help. When we were hooking things up, we took the Dynon alerts to an unswitched input, and the 396 XM radio to a music input on the 340. What I was told by my avionics guy is that music sources to a non-music input require amplification. Since your second Sig input is a music input, perhaps the reverse (or something like it) is at work here. Maybe hooking the Dynon source to the same (music) input on the Sig is driving the GPS audio way up. Have you tested the GPS audio without the Dynon audio attached?
You probably already know that you can put a 10K ohm variable resistor in the Dynon audio line. Maybe doing this will allow you to turn the Dynon audio down, and the Dynon and 496 audio will like each other better. This may be uneducated wishful thinking on my part though!
Another thought would be to look at one of Vern Little's Vx Aviation gadgets here:
http://www.vx-aviation.com/. Maybe look at the AMX-2A or AMX-1A. Vern would know best which one might help.
You've probably seen this, but just in case, I saw this site (below) with install guides for all kinds of Sig units...scroll down for the 200S stuff...includes the gouge for combinations with several radios.
http://www.sigtronics.com/air/tecavi.html
I'm sure you're wiser on this stuff than I am, but still hope this gives you a lead or two...or at least eliminates bogies on your way to a real solution!!
Cheers,
Bob