What version of Mumble are you using?
I recently started using Mumble again and realized that the "suppress" feature for PTT no longer exists. I went and grabbed the last version where this did work, 1.3.4
Here is a github with an MSI for that version. It might worth a shot trying an older version?
https://github.com/mumble-voip/mumble/releases/tag/1.3.4
Also, this might sound stupid but have you tried not using that audio software at all? I usually prefer to avoid those for reasons like this. If everything works without the software and you can just have a normal driver, then perhaps just avoid the software and the problem altogether. But I'm not sure if that will work for you.