Is a 45 degree mount an option? That way you don't have to raise the height of the scope so much, just slightly turn the gun and your able to use the red dot. If you have room for a red dot you should have room for a 45 degree mount.
For small red dots you have Trijicon RMR, Burris Fast Fire, Vortex Venom, SIG makes one as well. I'm not sure of any good budget versions of these but that's about the smallest your going to get. The 45 degree mount will allow for more budget options since you shouldn't have an issue of the scope being in the way and can choose a little higher red dot if you would like.
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