So here is my proposal:
When using the lensShift parameter, keep already rendered samples, and simply translate them to the new corresponding part of the image. The new regions that were not being sampled before could be dealt with by only sampling in the new regions until all regions have an equal s/px value.
The purpose of this is to save rendering time while being able to make a modification to the render.
Example: I begin rendering my scene, only to realize 5000 s/px later that one of my objects is slightly off the border of my render area.
Current solution: shift camera, re-render scene.
Proposed solution: shift camera, shift calculated samples over, gather new samples in unsample region (until caught up), continue rendering.
In Fig.1 I have A larger area than my chosen render size. The green indicates where I now want my render space to be, but only shifted, if I want to move my camera, the calculations for the image are different.
In Fig.2 The red region indicates which pixels/calculations I can save and not have to re-render and the pink region is where I need to collect new samples from
