Ceiling – Light replacement for a complicated light ceiling cover

Take the photo to several lighting fixture stores and ask. The staff will often have wide knowledge of back catalog.

In most cases it's more effective (insulation-wise) and cost effective to either insulate on top (Add sheets of rigid foam, plywood over, new roof surface on top of that) or to tear out the interior ceiling, insulate, and put up a new ceiling.

Depending on the structure, some sort of blown-in (cellulose, or fibreglass if you like insulation that gets less effective in the cold) is the only reasonable option without opening the ceiling up - you still have a bunch of holes you'll need to patch. Foam is problematic in closed-off spaces due to over-expansion. That is probably best hired - it's easy to DIY in an attic where you can see what you are doing, while blind insulating is helped by experience.

Or (rather less expensively) face the fact that the "room" is still really a screened porch (now with windows) and don't try to heat it in the winter - use the gas heater to extend fall and spring use a little, but close the door and leave it be in winter...Even with perfect roof insulation, a room with walls that are mostly windows is going to cost a LOT to heat in Massachusetts in the winter. Floor insulation, if any, is probably not great either, based on the porch conversions I've seen...