I experimented with these LED recessed lights that mount virtually flush, disappearing into the ceiling, as I renovated a detached structure to make an office and studio. I liked them so much ...

The Alcon 15100-R Linear Recessed LED Modular System offers an architectural-grade lighting system that his magnetically interchangeable for ease and customization.

I think your options are: 1) Retrofit PAR38 LED bulbs (similar to those linked), or 2) Take the whole fitting out of the ceiling and install a similarly sized LED replacement "can", with attendant ...