Recently, samples from different parts of cottonwood trees have been sequenced (Nature News). The conclusion:
> “The variation within a tree is as great as the variation across unrelated trees,” says Ken Paige, an evolutionary biologist at the University of Illinois at Urbana-Champaign, who led the team that made the discovery.
This doesn't say anything about overcoming self-incompatibility, and it probably depends on the mechanism of self-incompatibility if it can be overcome by accumulating mutations.