I ended up just going with the type s sway for now but can always upgrade alter if needed and yes it fits. I got my ASR from JHP.I'm going with that same setup - Type R sway with ASR brace, and did a lot of research. It should fit fine.
BTW - It's at JHPUSA for $181 with shipping included. That might save you a couple of bucks vs buying it at PJDM.