Cal -

If 1L was too small then I think you're definitely going to need a pack, I think all of the hydration units I've seen for vests are under 2L and usually 1L. You could probably also wear a tactical pack either under or over your vest to have even more options.

I'd personally look at Camelbak, they make hydration camo packs specifically for the hunting and tactical crowd. I'm not sure how how large the reservoir is on the hunting packs, but I know they make a 3-4L reservoir for their lightweight tactical models. Probably start around $75-100.

EDIT: I just found this Marchway tactical pack on Amazon. Appears to be highly rated, relatively cheap and the pockets look big enough to hold enough calls to work well for run & gun turkey hunting: