I did the rigid foam thing over part of my attic a few years back and I'd push back on it a bit before you commit. Stacked sheets on the floor look great on paper but they're a pain in practice. You have to cut around every duct, wire and vent pipe, and the seams will never be tight unless you foam each one. Then the stuff is slippery and crumbles at the edges the first time you crawl over it, and in most areas code wants it covered with something like plywood if the attic is ever used for storage or access.
Cost is the other shocker. Rigid foam gives you way less R-value per dollar than loose fill, so covering a whole floor gets expensive fast. What actually worked better for me was air sealing every top plate and wire hole with caulk first, then blowing in cellulose. Cellulose doesn't itch anything like fiberglass and it settles into a solid blanket over the ducts.
If the ductwork is what worries you, think about sealing and insulating the ducts themselves, or even moving toward a sealed and conditioned attic down the road. That solves the air quality issue at the source instead of hoping the insulation stays out of the air.