Experts and BHG readers answer.
Composting ground up stump material
I wouldn't bother with adding lime, as it doesn't seem to speed up the composting process. I would advise making large piles with thin layers of pine stumps plus soil, with grass clipping layers in between. This should break down fairly quickly and then can be used as a mulch for your new borders. The break-down will continue of course, and the product will gradually be taken into the new bed.