High No-Load Current on Transformers

No-load losses tend to be almost exclusively due to magnetizing current current, so the thing you should be looking at is how the cores for the high loss transformers differ from the normal loss ones.

You have to examine things that affect the magnetic path; i.e., the type of steel, the flux density, how the laminations are formed, trimmed, insulated, stacked, etc., how the core is shaped, clamped, bonded, grounded, etc., the positioning of the windings, the leads/interconnections, the type of fasteners, their positioning/insulation, are there any unintended magnetic paths/short circuits, hidden eddy current paths, even the material of the tank, the positioning of the phase leads/bushings, etc., etc.

Also remember that any losses manifest themselves as heat/hot spots, so you may find that untanking a unit and and doing a thermal scan may help pinpoint where the excess losses are occurring.

All this presupposes that you have done all the necessary steps to ensure that the transformer design and construction is correct.