Your experience is similar to mine. In an attempt to smash some stubborn brick walls, I recently visited the graveyard where many of my father's ancestors are buried, in the hope that an inscription might clarify family relationships. After a couple of hours of fruitless searching, I wandered in to the church, where the Sunday service had just finished. I asked if there was anyone who could help me locate the graves of my ancestors.
By a wonderful stroke of luck, they told me that the church archivist was in the church, and if I cared to wait, then she may be able to spare me a few minutes. The archivist found the burial records of my g.g. grandparents, and gave me the location of the grave (which unfortunately had been badly damaged in a storm in the 1980's, and was not recognisable). The archivist also looked in the records to find who else was in the grave, and found their grand-daughter who they never met, who died at the age of 4.
I left the archivist a list of other people that I was interested in, and some money to cover postage and expenses. I wasn't expecting too much to happen, but about a week later I received a letter giving me details of these people and (more intriguingly) who else was buried in their graves. Because the burial ground was inside the parish church, then all parishioners had the right to be buried there, but they did not get exclusivity unless they paid for a plot. The people buried in these graves helped me establish family connections - a niece buried in the grave of an uncle, and some people who didn't seem to be connected other than being great family friends who lived next door, and who baptised their children on the same days.
I hadn't persued the burial line of research too greatly until now, but the wealth of information I received means that I will certainly do it again (as soon as my health permits)