How can I finish an attic floor where the recessed lighting protrudes above the joists?
If the existing joists are adequate to support an attic floor, it will be far easier to replace the recessed can lights with wafer style LED lights such as these from Lithonia.  



When shopping, check carefully to see that the lights you select will work out with the openings in your ceiling.  You might want to bring one of the trims from your existing lights with you to the store.  

If the joists are too small and need to be beefed up, you can sister new, larger joists to the existing joists, but that will probably be a lot of work.