Just a couple of thoughts.
I see >90% success using simple cleft grafts. I think that it allows such a fast operation that it works better than the much fiddlier v-graft. Omega grafters are okay for thick stems, but suffer from the lignification and tough fibers often found there.
No need for whole plant humidity - 'though bagging above the graft is critical. I think active photosynthesis below the union is helpful to the scion, and have success in a space that's otherwise ~80F and 35% relative humidity.
It's far easier if the rootstock and scion tissues both remain soft/flexible. A rootstock that pumps sap instantly when cut is ideal.
And rather than use elaborate clips or wraps, I find that simply pinching a length of scotch tape around the graft works incredibly well (i.e., so that the sticky side meets on one side of the union). It's easy to apply a tight pinch to bind the union, and as the graft/stem swells, it'll shed the tape on its own!
Oh, and only one side of cambium needs to match, but at least one side absolutely must match. So different stem calipers are fine, but the lignification issue seems to limit very high % success with larger calipers, especially matched to much smaller scions. For cleft grafts, anyway.