Soooo many options to make it work on slippery surfaces! There is a silicon "pen" to add under knitted or sewn slippers, so they won't be so slippery. Or one could add a layer of leather (even faux leather would add a decent level of friction). Adhesive velcro. Or even just some straps to attach underneath a surface. Etc.
That's all fairly complex and kinda goes against my happy-go-lucky casual view of my crochet projects. I'll just put a pin in this design and come back to it when it makes sense with our decor.