Fishless cycle, qt after ich issue

New member, although I've been trolling for a while now. I have a 54 gallon corner that recently had an ich outbreak with one damsel surviving. I've since set up a hospital to treat the damsel, and a second tank for QT. I'm on day 8 of a fishless cycle adding majestic extra strength ammonia to start.

My display tank has been running since march, and fallow since early may. It initially cycled fast with the damsels after 2-3 weeks. My question is can I add one of the bio stars from the recently infected display tank to the bare bottomed empty QT to kick start the cycle without adding any ich to it. And if I do transfer the parasite, how long can it live without substrate or fish?

I would like to add fish within the next 3 weeks, just don't want to shoot myself in the foot by adding bacteria from a recently infected tank. 72 days from fallow will be July 19th, as I used some equipment that may have transferred some ich back to the display tank and pushed back my safe date.

Should I add some food instead and wait, or can I get away with a bio wheel to add bacteria now?

I've been adding stability, but no change in my ~3 ppm ammonia.

Thanks in advance.