I read your post with interest because I come from a small community outside of any corporate help in keeping the old cemetery. It's sad to see this happening in other places, too.
Here's what my community does:Every Memorial Day, people from there go back, (like a reunion)?The community has elected five local people toa "cemetery board" (one a sec'y/treasurer) and this board takes care of hiring the mowing done, with some maintenance etc.Also, at this time an accounting of receipts is given, open bank deposits/expenses shown to anyone. A Bank Account was set up at the local bank with Bank name posted on a sign on the cemetery fence,and anyone can send donations throughout the year directly to the bank. The board will then use the funds for maintenance.It has worked for this way for many years...People sometimes will give, but can't do the work.
Just an idea I share with you since you live far away.