>I had attached it on the seat stay, but that doesn't seem able to actually support it.
Doubt it ever will; those holes (with suspicious looking notch in l/h for a keyed binder bolt?) look bigger than any bolt you'd get into a seat stay, so you're not going to stop rotation, no matter how much MONGO you apply -
I'd guess you're missing a clamp that went around seatpost at required level (like above), thus allowing resting of protective covered (where the tape is wrapped) frame
against the stays.
Best bodge is couple of toestraps from the cross support rail up and threaded over the seatpost then saddle rails, just in front of the rail cradle.
Best solution - toss it in favour of something that works.