I continue to have good success with the modified bark graft, and have not noticed a problem with die-back of the rootstock wood at the union. Axier—are you completely wrapping the entire union (including the end of the cut stub) and scion with Parafilm so it doesn’t dry out?
Timing appears to be the critical factor for me—three of four grafts that I tried after the recipient tree had already leafed-out didn’t do much throughout the season, and then died over the winter. However, the ones I grafted just after the rootstock tree broke dormancy grew very well, and quickly produced strong unions. They also produced fruit the same season. I don’t see any advantage to grafting figs other than as a means of producing material to air-layer, but it seems to work well for that.
I’ve had 100% success using this method for persimmons, and it also worked on two out of four avocados I tried in the middle of winter, when a band of bark at the base of a small branch died and I wanted to experiment and see if I could salvage the growing tips. The scions were very thin—from toothpick diameter to about 1/8 inch, and the survivors are currently doing great on grocery store seedling rootstock.