The mentor method is an interesting concept that I saw last year and have thought about quite a bit. So far, the research isn’t very far along, so much of my thoughts are just speculation. To me, epigenetics is where there seems to be to be the best potential, which would relate to gene expression rather than transmission. I can see it having value in attempts to breed for a trait. For example, red flesh apples are something that I am experimenting with. I am planning to cross red flesh apples with sweet apples to try to get sweet red flesh apples. There could be some basis to think that grafting the seedlings onto a red flesh apple tree might help to enhance the expression of the red flesh genetics in the seedlings. In this sort of application, I do not see a big downside to using it as another tool in a project. The primary breeding method would be the cross pollination (genetics), and a secondary method would be the grafting of the young seedling to the red flesh apple tree (maybe allowing the mature red flesh tree to influence the seedling gene expression).
Another idea I have been thinking about is that it could be useful in breeding when cross pollination is not viable. For example, I have been considering aronia recently and it seems people have had success grafting pear to aronia but that there is difficulty in crossing pear and aronia. When pears are grafted to aronia, the pears are generally dwarfed and might fruit more quickly. Probably it is the case that the pear scion is not getting as much nutrition from the rootstock as it would from a pear root system. At the same time, the pear scion probably isn’t sending down sufficient nutrition to the roots because it would be using as much as possible, so I have seen some notes that it is worth leaving some of the aronia growth to support the overall plant (Aronia as rootstock - #33 by Sue-MiUPz3). Given all of this, I think it could be interpreted that pear is more nutrient demanding. I assume that aronia scion can be grafted to pear, but I haven’t seen any posts on this yet. In this case, I wonder if the aronia would grow more vigorously than normal. If it were to do so, then it might be suggestive of the pear rootstock giving a large amount of nutrition to the aronia scion. In that case, we might be able to use the mentor method to, over a couple generations, tweak the aronia gene expression to be more in line with the higher nutrient consumption of a pear. Purely speculating, but that might lead to larger sized aronia plants and larger fruit or higher fruit production all of which would be useful in aronia breeding. One user mentioned that pruning aronia into a tree form increased production (Goumi fruit - #182 by CoreFlex) which seems suggestive that nutrient concentration could have these effects.