Why a true Hood reconstruction required rebuilding her interior

What would a reconstruction have needed to change for Hood to cease being a battlecruiser?

It would have required stripping out and redesigning the ship's internal subdivision, not merely changing the external armour belt.

Hood's additional belt protection is described as a response imposed on a design already intended for a different armour scheme. The armour could be attached to the hull, but that did not redesign the internal arrangement behind it. To stop treating the ship as a battlecruiser in structural terms, a reconstruction would have to remove and rebuild much of her interior subdivision. An earlier answer adds that armour was part of the ship's fabric and that changing it so extensively could cost more than building a replacement. The example shows why a major survivability upgrade reaches far beyond replacing visible armour plate.