Can you add a photo of the area? Do the rocks heat up when the grill is in use? What is the soil like 3' or 4' from the stone wall? What are the sun and light levels like in the area you are considering planting? Do you have somewhere you could store a large pot for the winter such as an unheated garage?

Clematis can be grown in large pots (think whiskey barrel sized or larger), but might need some protection for the winter, either by insulating it where it is with something like bags of dry leaves or layers of bubble wrap. You also need to be careful of the soil mix you use - see the container gardening forum.

My thought is that you could plant your clematis out from the wall further. If you move the trellises out a foot or so from the wall, and then plant the clematis a foot or 18" from that, it will still be growing so it will cover the wall, but the plant will be in better soil. It may look a bit funny when the clematis are tiny, but once they fill in, it shouldn't be an issue at all. There's no reason that the clematis need to be right against the wall, and where you are digging right now, you are probably running into gravel added to help give the wall something solid to stand on.

I would also connect the three beds visible in the last picture, so there is just one bed that wraps around the stone-walled area. That would look better and be easier to maintain (mowing the grass in those corner bits would be a PITA!).

Thank you, NHBabs. Is there a low shrub you would recommend? And yes, we do plan on edging it :)

Depending on what you like,

one of the lower growing Deutzia such as Yuki Cherry or Chardonnay Pearls of Nikko, all blooming magnificently for a short period in midspring

a short Rhododendron such a Little Gem or PJM Checkmate

one of the shorter Wegeilas

Caaryopteris 'Sunshine Blue'

All of these grow just fine in my acid, sandy loam, but you should check locally to see what works in your area, since midwestern soils can be fairly different from New England.

Woody may have other suggestions since her soil is more like yours. I would use the same plant in both spots since everything else is symmetrical.