Well Francis...
1) What would be the affect of using 2gal of cider instead of 1gal cider and 1gal apple juice?
I believe the apple juice takes the tartness out of the shine, although if you want a little tartness, go with all cider. And it would make the shine really murky as opposed to a clearer look.
2a) How about doubling the everclear and leaving all else constant - would the apple flavor get too watery?
I tried this once...and it tasted nothing like apple pie. Just a too strong for me alcohol taste.
2b) If one started with more apple mixture and cooked it down slowly until some evaporated, would the resulting more potent apple mixture offset the increased everclear content?
Not sure how this would effect it, Everclear and Pinnacle are added the following morning after it's cooled down.
3) Ever try leaving the cinnamon sticks in the bottle of everclear for about a month prior to making the batches?
Might have to give this a try...