In case it sparks helpful ideas for you…

We did a to-the-studs remodel, demoing it all ourselves. We had a major mess with blown in (not foam) insulation.

The shop vac did not work at all. My husband ended up getting a 40’ length of black corrugated drainage pipe and duct taped it to the input of a dust collector from harbor freight. He took the collector bag off the fan and blew the output directly into a covered utility trailer he borrowed from a buddy. Hauled it to the dump.

Theres probably a less janky approach, but thats what we did.

If this is a big remodeling project you may well want to treat your lungs to a "powered air purifying resirator" 3M makes great ones (link for example purposes, shop around for a better deal), they cost a kilobuck and up but provide you with fresh hepa filtered air and are comfortable to work in in very dusty situations. Way cheaper than a hospital stay.

Look at adding a cyclone prefilter -- the Oneida Dust Deputy is one variant-- that will pull out 98% of the dust before it gets to your shop vac, then also splurge for the HEPA filter for the vac You don't want to be spreading that dust around, whatever it is. If the mess is more than shop vac sized then a dust collector may be the way to go.

The other approach is to spray it down with water using a garden sprayer to knock down the dust and shovel it out into trash bags, again avoiding spreading the dust everywhere.

I have an even jankier approach that successfully vacuumed up many bags of an unnamed insulation product. It is a homemade cyclone collector made with a 55 gallon drum, a piece of plywood for a lid, a garage door seal for a gasket, and some PVC pipe.

I have an even jankier approach that successfully vacuumed up many bags of an unnamed insulation product. It is a homemade cyclone collector made with a 55 gallon drum, a piece of plywood for a lid, a garage door seal for a gasket, and some PVC pipe. Just add shop vac.

Pictures are always helpful.