Wait, loose fill insulation? That stuff is the absolute worst to get out of anything. How did the cat even manage to dive that deep into it? Honestly, that's a whole different level of mess to clean up.
Seriously, I learned this the hard way last winter. My idiot cat got into the attic crawlspace and came out looking like a walking cotton candy nightmare. Took me three hours and two broken vacuum cleaners before I gave up. Now I just pretend the glittery fiberglass specks in my sofa are intentional decor. Some messes just win.
Intentional decor" is the perfect way to put it. You just have to surrender and call it a feature, not a bug, because that stuff migrates forever. I'm pretty sure my last apartment still has some of that glitter in the air.