A recent Instagram post indicates that she will remain in Houma, at the Thoma-Sea shipyard, until spring when the river rises sufficiently to get back on the cradle. The cradle has been refurbished and is ready.

Secondly, it took the shipyard more than 6 months to remove deck fittings (guns, sensors, lockers, etc.) in advance of the drydocking. They will be reinstalled after arrival back in Baton Rouge. [Lighter and easier to get back on the cradle?] IIRC, they contracted with the Texas to refurb some of the guns as the Texas' staff has current expertise. The Kidd will not reopen for some time after her return.

Rumor quash
1) They are not restoring the engines. Will never cruise on her own again.
2) The Navy is not reactivating her. She is a museum piece