It's good you brought up the issues with your radio as well. I think these two issues are very much related.
The EMS has issues if too much energy gets into the CHT/EGT wiring. Generally, this has been an issue on composite airplanes where the airframe doesn't block RF from the internal wiring.
In your case, you are getting this on a metal airplane, but you are also having transmit issues. This sounds a lot to me like the radio is transmitting a lot of its energy inside the plane, not outside like it should.
I really think you have an issue with your antenna or antenna wiring. Simple continuity checks aren't always enough with RF. Bad crimps, cables that have been crushed, or ground connections on only one end can cause big problems.
The easiest way to check this is with a VSWR meter, which an avionics shop should have. You may want to swing by one and get your antenna and cable checked. This measures the amount of energy that goes out the antenna vs. getting reflected back. Bad connections cause huge reflections.
Right now, you kind of have a virtual VSWR meter in the plane- your EMS! I assume you get the EGT/CHT rise on the ground, so you might want to play with your antenna cabling and see if changes help the EGT/CHT rise. I bet if you solve that issue, your transmissions will get better. One thing to consider is just running a commercially made BNC cable temporarily from the radio to the antenna as a test on the ground, to see if your cable has an issue.
There's no immediately logical way that a noisy ignition system can mess with transmissions. Noise messes with your reception, not your transmission. However, bad VSWR is much worse for transmission than reception. Plus, the Dynon radio is an awesome receiver so even with a bad antenna it's still pretty good.