greenman62 --
I'm really interested in this question too. I gather that not much specific is known about the interactions in figs. If you learn anything, please let the rest of us know. Meanwhile, I plan to start experimenting in a small way myself, grafting buds of later / less vigorous / more tasty varieties onto rootstocks of earlier / more vigorous and/or less tasty varieties. First I have to prove that I can graft successfully. Then I have to ripen some figs on the grafts.
For example, for buds: I have a 1-yr old Valle Negra that is a pretty plant but not a strong grower. It seems dwarfish (but without any obvious sign of disease). I may graft some buds onto a very strong grower just to see what happens. Ditto a 1-yr old JHA, which produced a couple of delicious figs but seems a mediocre grower. This year I started some additional cuttings of JHA, Smith, Norella, and St Rita just to have a supply of buds.
For root stock: I have an in-ground Hardy Chicago that seems inferior in taste to other Mt Etnas, so maybe I can trade up in taste by grafting on some St Rita or Norella. I have an extremely vigorous (and tasty) Paradiso but it is also very late; I'd never cannibalize the whole plant but maybe I can channel some of that vigor into a variety that is a bit earlier, such as JHA. In pots, I have some extra 1-year old cuttings of varieties that for me grew very vigorously (e.g., Black Greek, Emerald Green); and I started some extra new cuttings of early varieties (e.g., Florea, Improved Celeste). I may convert these to something else.
At minimum, I'm hoping to upgrade flavor on some rootstocks (e.g., HC --> Norella). I'm also hoping that the vigorous growers will impart that vigor to the weaker but tasty varieties (e.g., Paradiso --> Valle Negra). It would be a huge and unexpected bonus if any of the earliness of Florea or IC influenced the timing of the grafted buds (e.g., IC --> JHA).