sweet woodruff and dead nettle would both mix in with the existing vinca, and give you a three season ground cover that looks nice, smells nice, and is easy to maintain.

and oh, congratulations on getting access to your plot again...that must have been hard on the family.

Sweet woodruff likes it moist, though, so may not perform well in drought conditions.

I found this recommendation for creeping thyme (also deer resistant):
"Creeping thyme (Thymus vulgaris) has an unforgettable fragrance, is drough-tolerant and tends to stay shorter than catnip and sweet woodruff (about 6" x 6"), making it an ideal groundcover to plant in the cracks of a stone or patio floor, for instance. It is an herbaceous perennial in zones 5-9. Although it does flower, it is for its delicate foliage, culinary uses and aromatic quality that it is cultivated. Creeping thyme likes full sun and good drainage."

Here's the link, which also discusses sweet woodruff and catnip.
http://landscaping.about.com/cs/pestcontrol/a/deer_cover_5.htm

The sight of the earth settling on my son's grave for over a year unnerved me, so I planted Dragon's Blood sedum in the rectangle of bare earth. The site is on the top of a sunny hill and is subject to wind and no shade.

The sedum looked nice for awhile but clover eventually took over and now looks like the rest of the cemetery "lawn."

If you're planning on being more diligent in the maintenance of the area, sedum will work.

Thanks for all of the great ideas. I'll try some of the plants you all have suggested and we'll see what works best. The cemetery is on a farm adjoining ours so I can get to it rather often for maitenance. But the easier to care for, the better.

I grow all the ground covers mentioned here in zone 5a. Given the lighting you mention, I presume it to be partial sun to partial shade. Here's the scoop on them, with their soil requirements.

Sedum: needs full sun (6 hrs/day); any soil.

Thymus (thyme): full or nearly full sun; soil on the dry side, it will rot in too much moisture or shade (mine grows in gravelly soil, some of it in less than full sun where it does well); will inhibit grass; takes a while to establish; recommend woolly thyme or Thymus serpyllum (Mother of Thyme), 1-2" tall; evergreen; once established spreads vigorously; suppresses grass and other shallow rooted weeds but will harbor seeds of tap-rooted plants like Columbine; deer resistant (deer-proof for me).

Lamium (dead nettle): does best in bright shade; likes a rich (fertile, humusy); prefers moist soil (will tolerate some dryness but will not flourish); pretty good at suppressing grasses once it fills in; handsome in flower (white or pink); deer resistant (deer-proof for me). Should be mostly "evergreen" for you in zone 6 (KY).

Gallium (sweet woodruff): same light and soil conditions as Lamium; beautiful in flower (late spring); dies back in winter, re-emerges in early spring; self-sows and will "pop up" and spread in places that it likes; can be mowed (but why?); does not suppress grass, but almost does; deer resistant (deer-proof for me, and I love this stuff).

Asarum europaeum (European ginger): super attractive, and a favorite as well; a slow spreader but fills in densely; prefers partial to full shade and rich humusy soil, constantly moist (but not wet); grows so thick it suppresses just about everything; also check out the more readily available A. canadense (wild ginger). A.e. is evergreen and deer-resistant (although they nibble A.e. in winter, but it grows back just as densely come spring); A.c. is deciduous.

All like soil that drains well; all are easy to divide for propagation (anytime during the growing season); all hardy for you in KY; all (except Sedum and Thyme) will meet your light conditions; all are attractive, and, given the site, their habits are respectable. Note that only the Thyme can be walked upon (occassionally).

Yours idea is a kind and respectful one. If you can bring yourself to adding manure and/or compost to the planting areas, do so. Fertilizers should not be necessary (I never add them). Happy tending, and send us pics.

[Pics of Asarum and Gallium through google images or at my site: follow the link on "my page" to Rhododendron garden for Asarum e. or Woodland garden for Sweet Woodruff.]

A native sedum to consider: S. ternatum. It can take some shade as well as sun, and can handle more moisture than other Sedums. Also, I like Green and Gold, Chrysogonum virginianum. It's also native, evergreen, and has nice yellow flowers in the spring. There's a fast growing cultivar called 'Eco lacquered Spider'.

Creeping Phlox - beautiful flowers - all different colors - likes sun - looks good when not flowering.

This might help

https://theherbladyblog.wordpress.com/2017/09/05/wild-thyme-in-the-adirondacks/

Wild Portulaca?

At Riverside Cemetery in Denver, they grow a lot of Kannah Creek buckwheat because it's so drought-tolerant.

OT on the ground cover question, but I have to ask about the right to access cemeteries. Aren't they somehow protected? I thought if you bought property that contained a cemetery you were restricted in what you could do with it, which I would assume includes denying access. It seems as if the cemetery property was sold off from yours at some point. Is it possible there was even some agreement or easement included in the sale? I'd want to research this in all available records, out of curiosity if nothing else...

Are you asking if the cemetery was sold, would I still have access to the gravesite I purchased? Never entered my mind. Can't imagine anyone purchasing property that consists of only dirt drives and paths between graves. Interesting thought. Let us know what your research uncovers.

Strong agreement on ornamental native plants! These require almost no maintenance and their presence can be really poetic and beautiful in a cemetery. Where do you live (so appropriate suggestions can be made)?

Well-behaved naturalizing bulbs is another option. These don't provide year-round viewing but can be nice mixed with plants that pop up later in the season. Will it be a problem if plants reseed or somehow spread themselves everywhere? Seems very often the most low-maintenance plants, if they're non-native, have the highest potential for becoming weedy and invasive.

I would say thyme is a great choice. I was in Long Lake Cemetery in NY state not long ago visiting my ancestors graves. I noticed the whole lawn was thyme. I’m not sure which variety though.