"Republic of Texas: Poll Lists 1846" compiled by Marion Day Mullins, shows for Burleson Co, TX:
Gurthrie, George W. " John F. " William
Have you checked the Burleson Co, TX GenWeb site?Type in the surnames (use both spellings Swoap & Swoop) and you will find some interesting info on them.There is an index to the 1850 census, then you can see on the typed census record John Guthrie 41, b TN arrived in TX between 1834 & 1836 (ages of children).I think the other Guthries are too old to be his sons, so he may be an older brother, or maybe a cousin??The index shows Franklin Swoap, but name is spelled Sweap on the typed census.
I would go through any all county records I could find, especially land and probate.If the father did not go to TX and died with an estate in TN or AL, the heirs might give power of attorney to someone back home to collect their share of that estate.That should be recorded in land book in county where they resided, plus county where estate was settled.
Also, land records should give an indication when they first arrived in Burleson Co, TX.
Have you found a county history?Families there that early have a good chance of at least being mentioned.