The "climbing for altitude" makes it sound like a spinner. The fact that you don't see masses of the them rules out the white fly as far as I'm concerned. (Which are about a size 14 in the Mid-Atlantic -- although they can look bigger because they often don't completely shed their shucks in the dun-to-spinner process.)
I'd be thinking either Cream Cahill (a different species that the Light Cahill and very pale) or maybe even a Yellow Drake spinner (although it's getting a bit late in the season for them.) The latter are quite large.
Size 12 isn't large for a Cahill.
How many tails? Did you notice the legs?