Hi Brenda! First, I'm no relation, just a volunteer helper.
Now, I have some theories on this one; I hope you will keep an open mind about what I'm about to put forth!
I, like Joan, found Cassie's death certificate. What I was enthralled with was the name Thomas in the mother's name. So I started playing.
I looked in Mississippi marriage records for a Sullivan marrying a Thomas. Boom! I get a J. W. Sullivan marrying a Elizabeth Thomas in 1846 in Itwamba Co. MS!
Hmmm. Not a Z. Hmmm. But on further investigation of the 1870 census, I don't think that Z is a Z. I think it's a J. If you look at the original the other "J's" on the page have a similar loop that make them look like a cursive Z. Case in point...look at Jane's J. An if you check some other sites, like the Upshur Co. USGenweb, they index it as J. N.
So I go looking for some more proof. I find in 1850 John W. Sullivan, 25, in Itwamba Co. MS. With him is his wife Elizabeth, 26, b. AL with small children Julia, 4; Mary, 2; Malinda, 1. Also in the household in Barbara Sullivan, 66, b. PA. She's interesting. A grandmother? Mother? and the PA is very interesting.
So...we have John W. the right age, and Elizabeth the right age, (within a year) AND born in AL. Pretty interesting!
But! Not conclusive. Very circumstantial. It would need a lot of additional investigation to verify. I have looked all afternoon and can't find any other "bingo!" proof. =sigh=
I have some additional thoughts thoughts. First, since Allin/Allen/allan whatever is born in Texas, they may have been on the road for the 1860 census. But tax/land records in Upshur County may give some info.
Second, I have scoured the 1880 census. Nada. I think that your bunch might have moved over to Oklahoma, which, of course, was not enumerated in 1880. Part of my family is from the Fannin area and I know some of my kinfolks did.
Finally, Jane has me fascinated. Arkansas? What? They could hardly have been in Arkansas in 1849, then back to MS then over to AL then back to MS. Very unlikely. And why is she so out of order? On looking closely at it, I think that Jane's age is NOT 21, instead there's a cross through the 2 changing it to a 1. She's the baby. And they evidently ran over to Arkansas (which I have also had happen in my Lamar Co. TX bunch).
So, I have flown in the face of everything you had posted. But I think it's all something to think about. Funny how one word on one line of one death certificate can get all this going. But there you are.
Ideas for further investigation: obit for Cassie; tax and land records in Upshur; what happened to Josephine?; who is the person that is the informant on Linsey's death certificate?; and play around in Oklahoma and Arkansas. And I would also keep in mind that these folks are tumbleweeds (moving around a lot). Look in Lamar, Grayson, Red River etc. counties as well. I've checked a little on Lamar Co. USGenWeb. They have GREAT databases. I do have an Elizabeth Sullivan in one of the cemeteries, but she shows b. 1834 (d. 1900). That's a little late (but, then, you never know).