Lighting – Using metal paint can as cover for non-IC rated recessed lights

I am also in the Northeast and have had to tackle this type of situation a few times. There are several ways to attack it.

In your case, the best solution, but unfortunately the most expensive would be to use an open cell foam kit to fill the joist bays. They are fairly easy to use and give you about an R-4 rating per inch. They are a two tank kit with a hose and wand. Here is an example product: Touch N Seal 1000 Kit Open Cell Spray Foam Insulation

These type of kits start around $400, depending on the square footage and depth required.

A cheaper method would be to use 24 inch R-19 unfaced blanket insulation cut to your custom widths. You can use wire springs to hold it in place and keep it from falling. I would then cover the entire area with 4 to 6 mil plastic, stapled to all the joists. Tape the joints, if any. Moisture should not be a major problem since you have already done what sounds like a good job sealing the dirt floor. In the summer months, some ventilation in the crawl space will also help avoid excess moisture.

Rigid foam glued to the foundation walls would also help if the area is fairly air tight. If there is free air flow, insulating the brick walls would be a waste of time and money.

Yes you can sheet rock with longer screws. However the screws will basically have no hold until they hit the wood. Your previous insulation will continue to shrivel. Your ceiling will sag (glue and screw your drywall to ceilings). And you will be like - "why didn't I prep this for a couple hours so I don't have to redo it." Nothing worse than completing a job and knowing that something you did could (probably will) go wrong.

Also I doubt your insulation is even/flat and I think this would make hanging it flat very hard.

I am all about saving time but if you are in the house for more than a year or two I think you are wasting time.

Also why are you insulating the roof of a detached garage?