I have done a fair number of in-arch grafts on my own trees, (unappreciated destruction by round-headed apple borer eating all the cambium, following which the bark sloughs off). I am successful about 50% of the time. (Like you I generally surprise myself with how successful my scion grafts are - 100% with a recent batch of multiple pear cultivars)). I am not at all certain, but my sense is that one major factor in success is absolute immobilisation. Grafting a root sprout into a trunk which is bending in the wind poses a problem. And simply tight wrapping with electrical tape etc. does not stop the shearing effect of movement. I have never been able to drive nails in to hold the graft tight and immobile, but recently I have taken to using #5 1inch screws. (We in Canada have Robertson drive screws, which stay solidly on the end of the screwdriver. making it very easy to drive the screw straight. But that is a whole other subject.) This seems to provide the necessary rigid fixation.
Now the question of timing. I was confronted with this very question just yesterday. I don't (yet) have a definitive answer, but my reasoning was as follows: Budding is normally done in late July through August, (at least locally), so things will heal at this time. The bark is still slipping at this time, so getting cambium exposed on the stock is easy. The sap is actively flowing in the root sprout, so the graft union will be kept moist. Why not? I did it yesterday, and will let you know the results eventually. Meanwhile, my suggestion is to try it anyway - you have absolutely nothing to lose. And report back also.
One final point. If you are using an inverted-T cut in the stock bark, I
think one gets a better take by paring off the corners of the wedge cut on the sprout, so that there is cambium exposed on both the inner side of the graft and on the outer side where it is in contact with the back of the raised bark flap. But leave a "spine" of bark on the sprout where it is exposed by the bark flap on the stock being parted.
Broomholm OrchardZone 5b in Nova Scotia