Cathar, I just happened to think that piston pump idea you had wouldn't be to bad at all.
Piston pumps can operate very well at high pressure differentials, thus you could decrease the nozzle diameter on an impingement block design and decrease your nozzle spacing a bit to keep heat transfer uniform. That in turn would increase your exit velocity a ton! The boundary layer thickness would drop quite a bit and improve heat transfer immensely.
That doesn't even factor in the transient effects from the pulsating action of the pump, which won't hurt either.
OK, wow, I'm a nerd.... I'll stop now.