Last August, I watched a Long-tailed Giant Ichneumonid Wasp laying her eggs in the branch of a hickory in Green-Wood. (Spoiler: that’s not her above.)
But when she pulled her ovipositor out (first image), I thought, well, that’s rather short, isn’t it? I mean, for these Megarhyssa macrurus beasts. That shorter ovipositor, and the wing pattern, show this to actually be another species of Megarhyssa. This is Greene’s Giant Icnheumonid, M. greenei.
Megarhyssa are parasites of Pigeon Horntail larvae.
From bugguide.net:
Horntail adult females introduce wood-digesting fungi (e.g. Amylostereum) when ovipositing, which helps their grubs extract food value while feeding on the wood. Adult female Megarhyssa are able to detect the odor of these fungi, and once they land on the bark of an infected tree the Megarhyssa will walk along tapping the surface with their antennae (or “antennating”) to further pinpoint the location of horntail grubs within the wood.
Once grubs are located, the female Megarhyssa positions herself with back legs extended and ovipositor perpendicular to the bark, and drills into the tree to deposit an egg on or near a horntail grub within its burrow (see videos here). While drilling the female wasp is immobilized and vulnerable to predation by birds.
When the Megarhyssa egg hatches it behaves as an ectoparasitic idiobiont, completely consuming the grub. It pupates within the burrow and emerges in the summer.
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Backyard and Beyond 
Excellent photos and observations!
I saw two dragonflies with downturned abdomens yesterday at the Meer in Central Park. This wasp has the same bend. Is this typical of wasp and dragonfly females ready to lay eggs?
Sort of. Dragonflies don’t have long ovipositors, but they do bend their whole abdomen down to lay in the water, or wet vegetation, or soaking old wood (depending on the species). In some species, males will be nearby; others will continue to clasp female behind head as she lays eggs.