Ceiling material to use on cold joists
This tends to be a common sales pitch from insulation companies. You have now insulated your shingles. The danger is build-up of moisture in the sealed cavities. At least you are in a northern climate.

You are correct on #1. Dust and dirt will begin to form at the joists and studs on both the drywall and on the roofing surface (over time). You just need to paint more often.

Your option #2 is logical, but reduces the size of your room (as does #3)

Current thinking is to insulate your roof from the exterior with 2" foam panels. You then have air ventilation (in case of moisture build-up) both inside and outside (when using furring strips) of the roof substrate. Here is a sample of the design (see Figure 7): https://buildingscience.com/documents/reports/rr-0108-unvented-roof-systems/view

It's also in the current IBC code, so if you go to your building permit department, they should know the design or be able to look it up.