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Thyridopteryx sp.
This large, 1 in or 2.5 cm, caterpillar has attached a variety of leaves to its body.
Driveway
Psychidae, Thyridopteryx sp., and maybe even T. ephemeraeformis, though I am not fully sure do to the paleness of the marking on this individual. T. ephemeraeformis does not only feed on Evergreens, but also Oaks, of which appear to be attached to your caterpillar's bag. Awesome find, and congratulations on the move! :-)
A great hint that I thank you for sending. I have just moved and was trying to catch up on Project Noah work. I knew we had a few moths in North Texas that behaved this way, but could not focus my mind. It is probably a camouflaged looper (Synchlora aerata), I have most of its host plants and have seen it in the garden, but like Bugguide says you have to raise them to be sure.
You agree?? It was actually thought as a hint. I was not sure about that one. There might be other Geometridae/Geometrinae with such an interesting behaviour.