Unless we want to revise feigned history: The Middle Emnet did not exist as a separate entity before Eodwine was appointed as its eorl. There was no eorl at Scarburg because there was no eorl there at all. Not until Eodwine. This is covered toward the end of The Eorling Meadhall thread.
http://forum.barrowdowns.com/showthread.php?t=12545
See, Bethberry used to be the host of The White Horse Inn and asked me to take over. I did by replacing the White Horse Inn with The Eorling Mead Hall, but the way it was treated in the storyline was that Bethberry, the character who owned the Inn, sold it to Eodwine and went to visit her mother Goldberry (but that is another story). Anyway, to give The Eorling Mead Hall some reason to exist as the entity I had envisioned, I had Eomer create Eodwine as the eorl of the newly founded Middle Emnet.
It felt strange that the Eorling Mead Hall was in Edoras, just a walk away from Meduseld - which literally means Mead Hall in Anglo-Saxon. So when Sorn's land came free, I got to thinking that it made more sense for the Mead Hall of Middle Emnet to NOT be in Edoras, but in the middle of Middle Emnet. And it just so happened that Sorn's lands, which were renamed Scarburg, suited just right.
When Eodwine and company rescued Linduial, Sorn's keep was not burned down. So it got burned down in the short interim between then and Eodwine and company showing up there to live - a matter of months at most.
Hope that helps to give reasonable background.