I looked at the info on the people around her and didn't see a link, but you may want to look at them as well.
I think it's likely that the 2 Janes are the same (1880 and 1870). Maybe. That Arkansas birth in the 1870 census still makes me a little crazy. After all, they went out of their way to write 'Ark.' Wonder if it's possible Jane was a daughter-in-law? And I would sure look for divorce papers. My thought is the D in the 1880 census lookd a little weird...wonder if it's for widow'd. Maybe...none of this is making sense! On the flip side...wonder if Hatty is really Hatty Jane--she's the right age to be Jane 1 year old in 1870 and 10 in 1880 (I'm still clinging to my Baby Jane theory!).
Back to the Elizabeth in Hickory Grove in Lamar Co. Possibly, bears looking at, even if a long shot.
I knew somebody ended up in Oklahoma! And when I was typing out the previous post I started to suggest Yell Co. That was where my folks flip-flopped across to. Quite a migration pattern going there!