Amp question with size constraints

I am in the process of looking to upgrade my amplifier (presently a Rega Brio R), but I am faced with size constraints: given the built-ins I have, I cannot really go much beyond 13 inches in depth. The trouble of course is that better amps tend to be larger in size. 

To add another wrinkle, I primarily listen to vinyl (via custom Linn Sondek TT w/ MC cartridge and Fyne floorstanders). I've seen positive reviews of smaller Cambridge and NAD integrated amps, but they tend to focus on the digital side of things. What I'm wondering is whether an integrated amp with my size constraints would work well with my setup for vinyl, or alternatively if there is a good power amp within that scale that I could just pair with a decent phono preamp. 

I am not married to any particular approach but am not really sure which way to go at this point. Help me, Obi-Wan, etc.