A couple of random comments, based entirely on experience over a number of years, (no science whatsoever, and entirely anecdotal)
1) I have grafted with dormant scion wood in the orchard onto dormant root stock, at bud swell, leaf production, and, last year, in September. (I found some forgotten pear scion wood in the back of the fridge, it looked OK, so I experimentally stuck it onto an overgrown pear tree. All 3 grafts took and leafed out before winter arrived and the leaves shrivelled up, (but did not actually fall off - I think their seasonal timing got screwed up). I think 2 out of the 3 have probably died over the winter, but the 3'rd one looks healthy, with early bud swell). Bottom line: It is possible to graft successfully just about any time.
2) But my own experience is that I get the best take once the sap has started to flow in spring, but before the buds have fully burst. (This has an interesting corollary - should one actually prod one's bare root bench graft roots into activity for a week or so before grafting?? Would this improve take? [My sense is that apples are so forgiving that they take no matter what you do. But perhaps this would improve take on more difficult fruits])
3) My best success has been with whip and tongue grafts, even when the root stock is quite a bit bigger than the scion wood. But there clearly comes a point when the root stock simply cannot be cut, at which point my success with cleft grafts and bark grafts is pretty much equal. (This may be relevant with your over-grown thicket...)
4) I have salvaged old root stocks simply by treating them as trees, pruning them to form a framework, and then top working my desired cultivar onto the various limbs of the root stock tree. This being the case, you could quite safely move your trees to their permanent locations now, give them a few weeks to settle in, (and grow new roots), and then hack off limbs with enthusiasm and graft into the stubs. (You could reverse the order, and graft
in situ but my sense is that the trees are more tolerant of delayed grafting than of movement after they are actively growing.)
I have a minor distraction: I have just come from a talk by the fellow who runs Scionon. (They make rather slick grafting tools). He is adamant that it is essential to seal the top end of the scion. Failure to do so, he says, guarantees that the graft will dry out and fail. I have never done so. I generally get 90-95% take - are my failures the result of not sealing the cut ends? (I asked him whether he similarly sealed the ends of all his pruning cuts - he said, no, but didn't pick up on the parallel.)
Broomholm OrchardZone 5b in Nova Scotia