How do you dissolve 6 cups of sugar, into the SP for back sweetening, without either diluting it by using s simple syrup or shake/stirring where you're going to end up oxygenating it?
Personally, I wouldn't worry about the effects of oxygen from stirring on SP. However, if you are worried, you could simply be patient and let the sugar dissolve over time without stirring.
IMO, if you’re adding sugar in an attempt of chaptalization you could minimally add it to the must. Even without stirring it, the yeast will have their way with it up to their alcohol tolerance. However, oxygen during fermentation is necessary so have no fear stirring it up.