Gosh, that’s a tough one, indeed.
Maybe the batch-processor should throw an error:
ERROR: Input folders with different roots are not supported.
I think this case would still be ok:
with output folder:
D:\Output one would get:
In fact, I kind of like keeping the original file extension (first version) because it makes it super obvious what the input file really was.
Now that I look at it, your original example could be handled like this: