Oh that made me laugh so hard---you see I have a kitty that could be a twin to yours. AND she delights in playing in my fabric pieces. If I had strips on a stand like that she would be doing just what yours is, as she is a total acrobat. Can get into some of the most weird positions. Even found her on the top shelf of the closet one day, the door had been left ajar and she slipped in. Was fun getting her down too as she decided she had forgotten how she got up there and was complaining.
I hope you get your strips all sorted again.