Improving transformer voltage regulation / efficiency through construction
The best that can be done during manufacturing is to build the equipment according to the design.
These characteristics are defined during the design stage.
Voltage regulation depends mainly on the leakage impedance, so reducing the stray field reduces the voltage drop. The main way to reduce the stray field is to use fewer turns or to bring the primary and secondary windings closer together. Of course there is trade-offs, a very low impedance creates problems for protection, as in the definition of the circuit breakers and very close windings can cause electrical discharges between them. (in small transformers, such as less than 45kVA, the resistance can considerably influence, in this case, using larger conductors helps).
As for efficiency, it is necessary to reduce losses. This can be achieved using better materials (like copper instead of aluminum for conductors or more refined silicon-steel for the core) or more material, increasing the amount of silicon steel (which ends up reducing the magnetic flux density) or the amount of conductor (which reduces loss by Joule effect).