WIth that lens, I would go with an A19, but you could also chance a BR30. I seriously doubt that a BR40 would work with that lens.
Off topic: I replaced some expensive Lightolier non-ic remodelers that some dingbat had installed in our living room. If you pulled the trim down, you could see the rafters, so they had to go. I wanted to replace them with ICAT rated Lightoliers (1100IC), but they were fairly expensive, so I replaced them with Halo H7ICAT, which were a fraction of the cost. The H7ICAT are rated for BR40s (which we had been using with the Lightoliers), but that is baloney: with a BR40, the bulbs hang down below the ceiling, causing massive glare issues. Of course, I didn't discover that until I installed them, muddle around the holes (a slightly smaller diameter than the Lightoliers), etc. Luckilly, Lighting Science / Ecosmart made a BR40 that was as short as a PAR38, so I used those, but my stockpile is running out after 3-4 years of near-constant use.
You can make the BR40s recess more, but it involves drilling and installing a new adjustment bolt higher in the can. I wouldn't do that with incadescent or halogen bulbs, as that would bring them too close to the top of the can, causing the temperature switch to trip (at best) or a fire (at worst). But, since LEDs put out a lot less heat, I doubt recessing them more woudl be an issue.