Rather than keyframe with Constant interpolation, you can simply keyframe normally (using smooth interpolation) and add a modifier to your f-curves to mimic the 'jumpiness' of stop-motion.
The modifier you need to use is the Stepped Interpolation modifier. This modifier takes your f-curve and splits it into time slices based on the Step Size, retaining the value at the start of that 'slice' for the duration of that 'slice' exactly as how you are currently doing with 'constant' interpolation.
You will need to add the modifier to each f-curve in the Graph Editor and set the Step Size to the same value for each.
Note : For added versatility you could potentially use a Driver to set the Step Size based on a single custom property in your scene. This way you can easily adjust the stop-motion frame rate for your whole animation rather than having to change each modifier individually.