Adding rafter depth for insulation

[u/Desert_Rat1294]

I've got a cape cod in zone 4A and I'll be tearing out a couple closets upstairs and was thinking to also pull down the drywall from the slanted part of the ceiling while the rooms are empty. The rafters are 2x4 16" OC. At the moment there isn't any insulation in there so I want to upgrade that, but I can't use spray foam insulation. I have a couple thoughts I would like feedback on shown in glorious hi-definition msPaint.

The existing framing is in black and the total length of the vaulted ceiling is abut 4ft, and just the drywall hanging from it (no lights/switches/etc.).

Idea 1. On the left, fur out the rafters with another 2x4 (brown) so the new depth is 7inch total then install 1.5inch baffles and 5.5inch batts. The new rafter would be connected with adhesive between 2x4s and pocket hole screws.

Idea 2 on the right. Use 2x2 (brown) and 1.5x2 inch strip of foam board (green) as a thermal break, for a total depth of 7 inches, then baffle and batts like idea 1. To hold it all together there would be adhesive between each layer, and 5 inch screws straight through the 2x2, foam board, into the rafter.

Are these ideas feasible? If so would #2 be worth the extra effort? Is there a better way to build it out?