Tall Fescue, mostly Pennington Seed's Rebel, but occasionally I've also used Lesco's seed. I have a lot of large trees, and although the grass seems to be ok in the open area, the turf doesn't last through the summer in the shady areas under the trees. I have also tried perennial rye, but that didn't seem to work very well. It seemed to me that the TTF provided better results and lasted longer. Last summer I also got hit pretty hard with crab grass in about a thousand or two square feet, so in the last few days I have already hit those areas with some Snapshot, and I thought I'd wait a few weeks before using seed there. But meanwhile, I thought I could start on the bare spots under the trees and on the fresh-dirt section that I recently cleared of decades-old layer of fallen leaves. Well, anyway, I just thought that maybe I could try something other than the Pennington or the Lesco this year. Any advice would be appreciated. By the way, I've already, in years past, done the soil test and add lime procedure. I get grass every time I try, but it just doesn't last.
You say you've been adding lime to raise pH in the past, but what kind of soil do you generally have....clayey, silty, sandy, rocky mix?
Do you aerate this lawn regularly?
The shaded areas under the trees...
What specie(s) of trees are you dealing with?
Do you have stuff like black locust, ash, or hickory that'll let enough light through to grow grass?
Or are you fighting the losing battle caused by the grass-smothering canopy of a red, sugar or Norway maple?
You are absolutely right about fescue in shade.
TTT fescue has been shown over & over again at the Ohio Turfgrass Foundation's shade test plot near Columbus OH, to be superior year after year in comparison to species like CR fescue, bluegrass.
Granted, the shade they have above those plots is produced by a natural line of black locust trees. Your shade situation could be MUCH MUCH deeper!
Recommendation: Keep adding DIFFERENT fescue varieties to add... "strength by number of species".
Not to discourage you too much, but you'll likely never see a healthy stand of grass growing right smack in the middle of a forest, at least not in this latitude.
You applied Snapshot to turf?

You sure you got that name right?
Maybe you really meant something else?
If you want to have a little fun, take 1/2 hour or so and dig into this!
http://www.ntep.org/
I had to go back into it myself this afternoon for something, so I made notes of NJ-specific or shade-specific reference points along the way for you.
Here you go:
P. 31-33 shade in Ill.
P. 34-36 traffic stess in N. Brunswick NJ
P. 92-93 total establishment (look for "NJ2")
P. 112....summary
If they're still available in your area, I'd place my money on high-performing individual fescue varieties like Turbo, Spyder, Rhambler & Wolfpack.
You may have to call around to different vendors.
Some of them will sell a single variety in one bag or out of a trash can (a monoculture).
Others, Like Lesco / Deere, try to stick to the wise rule of " having strength in numbers", by selling only in
mixes or blends of seed varieties.
FYI....a "blend" is two or more of the
same species in the same bag. (Like two fescues or more, a "polyculture"

)
A "mix" of seed is a
multiple of species mixed together in one bag. Like two fescues, a bluegrass, and a perennial rye.