Sent you an e-mail today which made me think of the Davisson family so took a look at what was posted and saw yours.
I took a look at the 1900 census for William A. and wife Mary C. It does looks like they would be the right family. William A and Mary C. have same initials as in 1880 and right birthplaces and right ages. Also, as you say, son Perry went to NE. They are in the right area of NE too - Butler Co. So, everything looks right.
I'm not sure what you have. You mention the family may have gone to MO and back. I looked at the 1900 and then followed the sons (as I didn't know daughters married names) and see that Amos stayed in NE.
Jacob went to MO and is listed with his parents in 1910 and his mother is with him in 1920 and 1930.
Let me know if you want me to send you those census records. I also found WW1 draft registration cards for both Amos ( which shows father as in MO) and Jacob. Jacob is in MO and says he supports his father and mother.
I have been trying to find a way to confirm that they are brothers of Perry. I had hoped the family would be in 1885 NE census, but I guess they had not arrived there yet.
I am going to keep digging so will let you know what I find, if anything.