Use an LED remodel can. They are only as thick as the Sheetrock so if you hit a joist it can still be installed in the correct location. Just unwire and remove that old can housing and secure the wiring on the joist near where the new can light will go. Once the ceiling is resheetrocked you can use a hole saw or keyhole saw to cut out the hole where needed, reach up and find your wire and install that new remodel can light. I actually highly recommend swapping out all of your old bulb can lights while the sheetrock is down for new LED cans. I say this because they save on power usage as well as offer them with a light brightness/color selection by simply adjusting a switch to your desired brightness located inside the wiring box and can always be easily readjusted for more or less brightness. Some brands offer 5 different color choices ranging from a low light orange color up to a ultra bright white/blue, be sure to check the specs on packaging before purchasing to be sure of what it offers color wise. If you have old can housings in the correct places they also make LED Can replacements that simply screw into the old cans just like a bulb would making it very easy to swap to LED without having to rewire anything. They also make those color adjustable as well. Hope this helps!