The TurtleLady stand in my living room has a similarly narrow stance. The tripods are made of maple saplings and I screwed smaller sticks to the legs to keep them from "walking" inward.
I took advantage of the sticks and made a "kitty hammock" on one of the tripods by stretching a piece of fabric around the sticks:
The sticks also stiffen the legs of the tripods. Of course, this makes the stand decidedly NOT portable, but--for me--that's okay. It serves its purpose in my living room nightly. Good luck!
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