John said: It's cool enough that we won't be stressing the plants.

I don't think that's how it works unless your reading about sheltered apple trees such as in a greenhouse because the cool weather you speak of invites the end of the growing season with rain, and with that a new tide of disease. The rain is like a new environment to the apple that could exceed to the apple that stress you caused by what you grafted this spring. 

If you did do it the way you propose, I think I would advise all to put a temporary rain cover for about 30 days on the apple tree in it's new location. Generally 30 days should be enough to re-associate with helpful soil microbes by that time and as such these new associations will relieve all outdoorsy concerns. 

A slightly different tangent, I'm glad we understand that we never transplant in the growing season because if we did this we would soon find out that the early seasons growth are excessively stressful events once the roots get disturbed at that time.

I consider about what I touched on as more an important 'concept' rather than an idea. The latter seems more imaginitive while the former more based on real life or past examples.

Speaking about practical examples...

For a while I was growing pawpaws from seeds and when fully dormant I thought I could unearth them in mid winter and sell them for a buck each to a plant nursery across the street. The soil was never dry, and in fact very loose and perfect to pull them as seedlings that were past two leaf seasons. So they accepted them for (fortunately as a gift) but later that year Bruce the expert over there said they died like so many in the field would warn this to happen.

So with that then why is it that an apple tree but not a pawpaw can be moved. So to get to the bottom of these differences (apple vs. pawpaw) is an idea as kind of an extension to the original concept of what we were mentioning. Which is to say that pawpaw roots go completely dormant in mid winter where as apple stay above completely dormant. 

Half of what I just said must go along with another similar example about how farmers bench graft apples. In that case the bench graft protocol is to bareroot the apple seedling in December, bring that onto a grafting bench in a cool garage, graft it, then finally leave it therr fot one month (ie. the 30 days) for callousing together. 

As seen by this process is the omission of placing them outside until the combined two stresses have recovered from the both shocks. 

Further seen is the idea that you could never recover into a new environment (ie. placing apple outside in 30 days) if roots were in the 100% dormant state the way I suspect of pawpaws.

This is out of the box somewhat but it aligns in many other scientific ways too.