We put in a front yard paver patio a few years ago. The edge facing out to the street is zig zag. For whatever unknown reason, we have been unable to get grass growing in the zags, even though there was grass growing normally there before. The grade was slightly changed and we installed sod right after it was done. The sod looked fine but by the next spring was dead. Then we tried seed for a few years. All dead. The area occupied is basically 3 three foot square sections. Two sides of each are bounded by the pavers, one side by garden bed, and the remaining is the rest of the lawn.
I am ready to give up on grass for these sections. I could just expand the garden to fill these nooks, but it is necessary to drag the hose across at least 2 of them to water a bed on the other side. So anything I put there really needs to be short or hose proof. Conditions are mid morning sun til about 2 pm, then house shade afterward. It can be very hot in the summer. This area gets watered a lot, though, as I have patio planters in abundance.

I have a fancy leaved English ivy in one bed. I thought it would not survive the winters but it has done well. I could take cuttings but I'm not sure I want something long and vine-y in that area though.

Any suggestions? I'm not really interested in the common ground covers like pachysandra or vinca.

Visiting the Missouri Botanic Garden recently I saw a plant that I thought looked promising: Ajuga Mahogany. It looks a lot like purple baby leaf lettuce. I have Ajuga Chocolate Chip in another garden, and have not been that impressed with it. But the A. Mahogany was short (~ 3") and very full. It is also a brownish purple that would go GREAT with the heucheras I have. Anyone grow this?

Thanks for your ideas for what is really a weird situation.