In the past, I've replaced old incandescent can lights with LEDs and it has been a breeze.

For the latest can light I'm replacing though, the attachment is different and I can't find an LED retrofit that would seem to work.

This is the inside of the current can:

Here is a typical retrofit LED:

The can doesn't have the holes on the side for the prongs of the retrofit LED. Instead there are some clips right next to the light socket. There are also the vertical slots closer to the bottom of the can but I don't know what they are for.

Is there a way to attach this LED to this can? Another LED that would work? Or am I out of luck?