How much closed cell expanding foam insulation do I need

At this point, it's not a DIY project. You need to consult an engineer or an architect/engineer that is used to these kind of building envelopes. A sealed envelope with an ERV needs to be designed and PROPERLY sealed, and the ERV capacity needs to be determined and designed by an engineer in order to meet building code and pass inspections.

Note: I'm in TX and familiar with building code for high efficiency projects here, and my girlfriend is a PE but not in HVAC.

Skip the expanding foam and buy pre-made foam panels from your local HI store. Layer them up for more insulation and cut them to size with a knife or saw (I just use a drywall saw). You can enclose them in a wood box on top if you'd like, but they're rigid enough that they'll stay where you leave them without building an enclosure (unless you turn the fan on).

Just saw your edit about the motor. You can build up the foam panels into a tent. But if you can get a cover designed for a whole house fan, that may be your best option.