The more I look into this, the more I think the scenario where Sears Holdings buys back Transform Holdco holds strong.
Transform Holdco is not publicly traded. Complying with the continuity of interest (COI) requirements, so that NOLs are preserved, means they will need to offer non publicly traded stocks to old shareholders. That is not practically feasible. A 100% cash offer does not comply with the COI requirement. The only possibility left is for Transform Holdco to elect to a Designated Sale Transaction, ie leave the NOLs with SHLDQ as part of the Asset Purchase Agreement, and then for SHLDQ to buy out Transform Holdco.