How can I fix HDMI audio splitter creating 'Ghost Monitor' on Mac Studio with multiple displays?

I recently replaced my old Mac Pro with a Mac Studio. What I did not know is that Apple had ditched the older but otherwise very handy dual analog/optical 1/8’’ ports with less capable analog-only ports. This rendered my extensive, TOS link-driven surround speaker system nearly useless, from 6.1 channels to 2.0 in the name of “upgrading.” (Shame on me for not having researched this further before upgrading.)

This left me looking at the HDMI port for answers. I found a splitter that separates an HDMI signal from the Studio into audio and video signals, and the audio output has both a TOS Link and digital coax option, so my speaker system is back in business. The drawback, however, is that using the splitter tells the Studio that there is another monitor attached and adds a “ghost” part of the desktop that complicates my three Thunderbolt monitor set-up. One constantly loses track of the mouse pointer, among other irritations.

So, my question is whether there is a software or hardware fix to eliminate this invisible monitor while keeping my speakers booming at full capacity? I could not find a splitter/extractor that pulled only the audio signal from HDMI.

My thanks in advance,

[Re-Titled by Moderator]