Agree with 3M 77 - just used it on the carpet that goes over the ceiling of my Uhaul
where I had to pull it back for my window repair.
Another option could also be to glue velcro to the walls then attach the other side of the velcro to the hides. - This could allow for greater ease of removal if needed for wiring, cleaning etc. But the hides could sag in places depending on how you do it. I have just sewn grippy velcro onto vintage travel pennants and used this to attach them to the carpet on the ceiling in my Uhaul
Sounds like a fun project.