I found a pre that meets your size criteria:
The Outlaw 975 preamp is only 10" deep!
Unfortunately it is out of stock which, in todays uncertain times could mean many things, but call them to see when you get the chance.
You would still need an amp, but I think finding an amp that is 12" deep would be easier than the pre, so think there may be some decent options. I know Crown makes some pro amps hat are about 10" deep, but they are 19" wide (I don't know if the rack "ears" can be removed), but I think the 975 is a promising option!