TrainsButSmall
I get that there are almost no surviving transformers, but you could build a new one to the original design (excluding the oil). Would this work?
The answer is a bit complicated.
The original transformers were designed, and their very complicated frame, winding/tapping, and insulating structure designed around, the use of Pyranol as the transformer 'oil'. This had high-temperature, high-current advantages.
https://steampoweredradio.com/pdf/general%20electric/components/general%20electric/General%20Electric%20Pyranol%20Transformers%20Including%20Pyranol%20Immersed%20Current%20Limiting%20Reactors%20Instructions.pdf
The stated reason for not replacing the 'fluid' was that it was technically impossible to remove much of the Pyranol, more precisely its degradation products (dioxin and furan), from the transformer internal structure without compromising it electrically. This was not a decision reached lightly or 'solely by nanny-state bureaucrats'.
Theoretically yes, you could build a replacement transformer that would run a GG1 in excursion service. It would still need to be oil-cooled. I have not looked to see if modern replacements that perform as well as Pyranol have been developed in recent years, but designing to lower amperage requirements should allow equivalent tap structure, and I think there are clearly better internal insulation materials for actual fabrication.
https://www.usbr.gov/research/publications/download_product.cfm?id=2822
The principal issue is cost. Building one of these is a complex, safety-critical operation ... and when you're done it would be restricted to 25Hz and no more than 12.5kV, ruling out both most mainline operation and cost-effective museum operation at the same time.
Redesign of the main transformer to 25kV is an obvious improvement; detail design could probably be made through nothing more complicated than a good college engineering contest backed up by expert design analysis. But here again, construction of the new machine followed by careful rebuilding of the rest of the running gear would likely involve multiple millions of dollars, followed by expensive regular maintenance.
As some have pointed out, it would be cheaper to adapt other components, one example being Mr. Klepper's adaptation of AEM-7 electrics to supply filtered DC to the GG1's universal twin motors. (The problem there being that Amtrak, for somewhat misguided liability reasons, does not allow sale of any of its locomotives for subsequent operation; they went so far in a couple of the early scrappings to cut the wheelset axles and side frames to rule out their being adapted to any operable purpose...)
Note also that the New Haven prototype from which the GG1 was taken had arrangements to use NYC 750VDC third-rail power from New Rochelle via Woodlawn, far more than just 'accommodation' to negotiate the Park Avenue viaduct at its restricted speed. So logically any museum with 600V trolley power and overhead suitable for pans could arrange for a G to be, comparatively easily, 'reworked' to motor a couple of axles without grossly overloading things...