Sverre-
Couple of things. A short barrel might give a little more recoil, due to lighter weight, but what you really are probably noticing is increased muzzle blast / flash. Make sure you wear good hearing protection. In a double action gun, recoil is best handled with a rubber type grip that covers the backstrap, especially the recoil hump - it helps spread out the surface area and gives a little under recoil. A padded glove may also help.
If you are getting 1300fps in a 4 inch Smith with a 300 grn bullet, that's hot. I would load it down to around 1150 fps or so and call it good. A hard cast, or strong jacketed bullet at that speed will penetrate like crazy, and handle any need short of a Texas heart shot on a moose.
Sight in for the 300 grn. / 1150 fps. load, then load a bunch more at about 900 fps, and practice with those loads. There is a lot to be said for practicing with the load you are going to use for combat shooting, but for big game, you are not going to be engaging multiple targets, or shooting fast triple taps double action...
Larry