A while back, I had bought a bunch of scrap packing foam, without any specific sound properties, but one side has a nice, wavy, dimpling pattern, so I can address large flat surfaces like the ceiling.
Mounting trial 1: Two-sided tape. Separates from the foam after a few hours.
Mounting trial 2: Tape plus cards with slits cut, then tuck corners of foam into slits. Worked great, but was advised of poor esthetics. Plus, I could see I'd quickly run into a tiling problem.
Mounting trial 3: Clear packing tape over foam. Worked great; minor esthetics issue. If trial 4 fails, we'll return to this.
Mounting trial 4: Stronger two-sided tape. So far, so good.
Next up: "Hiding" walls and doors from the mic, using a somewhat-portable frame upon which I'll hang old blankets, etc. Cat Lady and I met with a friend at Lowe's to buy lumber and other materials. I sketched this rough schematic (of one of the three panels) for him to follow when he builds this for me:
Then, I built a sort of open box on top of my kitty litter microphone mount using a few panels of Auralex foam, to block sound reflections from behind and around the mic. This actually worked stunningly well, (people swear by Auralex), except for the little fact that now I can't keep my mouth close to the mic and be able to read scripts at the same time. I'm going to have to modify the box so I can see, plus add my new pop filter, but here's where it stands now; you can still see the kitty litter jug at the bottom: