I find that the choice of gun can make a big difference. I also have short fingers, and there are simply some guns I can't shoot well.
Shooting a large frame (N-frame) Smith & Wesson revolver double action or some of the large DA semi-autos is pretty much a lost cause for me. But K-frame S&Ws, 1911s (specially with a short trigger), Glock 17s or 19s, and other guns of similar size and trigger reach I can manage well with proper placement of the trigger finger on the trigger. Grips can also make a difference.
The key is to be able to press the trigger smoothly straight back, with only the trigger finger moving.
"It is long been a principle of ours that one is no more armed because he has possession of a firearm than he is a musician because he owns a piano. There is no point in having a gun if you are not capable of using it skillfully." -- Jeff Cooper