I agree about the mechanics involved. The recoil was lateral force backwards and also down, through flex in the carriage and axle. A field gun on the AnXi carriage had 10degree of elevation and about 15 degrees depression from the horizontal on horizontal ground. Making the tube horizontal of course requires more elevation or depression depending on the slop/inclination of the ground. This is covered in the French 1824 artillery manual.
I have test data concerning testing axles in 1802 comparing elevation, number of shots at each elevation and number of shots to fracture an axle if that is any use. If memory serves any elevation beyond 8 degrees fracture the axle be it field gun or howitzer, thus both fired on similar trajectories.
Mortars, the mortar bed preparation I assume being a reason why they were not used on the battlefield