First -- what time period are we talking about? For the first 150-200 years Quakers did not mark graves with tombstones; even when they did begin marking them, they were typically very, very small and simple until the late 1800s when they began to follow more mainstream burial customs. However, Quakers did maintain very extensive and thorough birth, marriage and death records, many of which are still extant and available either through Ancestry.com, through individual meetings in a few cases (if the meetings are still extant), or through Quaker College archives (e.g., try Haverford or Swarthmore for Pennsylvania Quakers). There are also some very extensive abstracts of Quaker records published by a man named Hinshaw that may be helpful to you if your ancestors were indeed Quaker for a time.
Whether or not Quakers were persecuted depends on where in the American colonies you are concerned with. They founded Pennsylvania, and so were not persecuted there or in Delaware or Rhode Island. I do not know to what extent the settlers of New Sweden were subsequently absorbed into Quakerism following the arrival of William Penn. However, they probably followed similar migration routes into the continental interior whether they converted to Quakerism or not. Early on, Quakers were very severely persecuted in Massachusetts and Virginia. However, I believe the persecution in Virginia primarily predated the early 1700s and was mostly in the Piedmont region as opposed to the Appalachian part of Virginia that subsequently became West Virginia. Quakers followed a couple major migration routes. Early on there was a north-to-south migration from Delaware and the Philadelphia area southward as far as the Carolinas. Later, as American civilization spread westward, the Quakers did, as well. Some migrated from eastern and southern Pennsylvania into the panhandle of Maryland and western Virginia and down as far as western North Carolina -- this sounds most similar to what you describe. Squire Boone (Daniel's father) followed such a route before his son pioneered the migration route through Cumberland Gap into Kentucky. Few Quakers stopped in Kentucky, however. Rather most wound up in Ohio or Indiana, where they converged with other groups of Quakers migrating westward from Pennsylvania along the National Road.
Hope this may help