How larger infrastructure changes post-Hood capital ships

Would upgraded imperial infrastructure push Britain toward the larger K2, K3, and L2 post-Hood designs?

Yes. With adequate infrastructure, Britain would favour the larger designs and might pursue even bigger ships.

A British Empire that upgraded docks and shipbuilding infrastructure could pursue K2, K3, L2, and similar large post-Hood designs. With those physical limits eased, the Admiralty would prefer the larger options and might go larger still. Paper characteristics mattered only when yards and docks could build and support the hull.