I haven't done Citrus grafting recently, a procedure that worked very well was a side bark graft when the rootstock cambium was slippery and moist. I made a shallow downward cut just under the bark, trying not to harm the underlying wood. Next, I selected the thinnest, flattest scion I could find and shaved the outer layer of both flat sides of the scion, exposing, but not removing the cambium. Then slipped it under the bark flap I had created. Due to the thin scion there was very little bulge after insertion. Next I wrapped the graft area, being careful to match the wrapping tension to the robustness of the grafted tissues. Tender parts needed less tension, thicker required more.
This was very successful for me, on the other hand persimmons with cold damaged cambium were pretty much impossible to get to succeed.