I have a thompson center prohunter with a 22-250 barrel on it. I have a nikon buckmaster 4-12x50 scope to go with it. Would a medium set on DNZ mounts work or will i have to go with the high mounts.

although I am not certain I am thinking it would work. I use low mounts on all my encores. I have a big 50 mm 8.5 x 25 Mueller scope on my 22-250 with low talley mounts and it is very close.
I have DNZ on my375 H&H barrel...very nice equipment.

I have a medium DNZ on my Savage 220f with a Leupold VX-II 3-9x40, I would contact DNZ with your info just to play it safe, they will let you know what to use

I have a set on my Whelen ProHunter with a Nikon 3x9x50 I had to go with the high ones on mine.