Again, thanks for the replies, everyone. Really helpful.
Unfortunately, we don’t have a huge budget for this project, so many of the more permanent fixes are out of our price range for now, though they are good recommendations.
I suppose the guy we had finish the room didn’t install insulation because the the lights needed to vent. Back when we first finished the room, before the present heyday of energy-saving lights, the lights in those cans generated enormous amounts of heat.
If we do put down spray insulation, I’ll be sure to see about getting a moisture barrier to keep mold away.
I’ll be coming back to this thread as we consider other fixes, too.
For now, I think we’re going to do the window film and the foam circles in the cans.
Thanks freepers!
As you can see, you will get many different suggestions.
Since you have decided to address the recessed lights as a first step I suggest you go to Home Depot and get the new replacement lamps they sell which cost about $40 each. They are LEDs and turn a standard RC light into an air tight fixture. Installation is a snap - there are videos on Youtube and Home Depot has one on their website.
If you are going to go for a more detailed approach then the advice a poster mentioned above about having a professional advise you to avoid problems down the road (mildew, mold) is spot on.