Niagara Generator has a home page and appears to have a customer service number. Sears looks like it sells parts for some Niagara/Generac generators. Contacting either may yield a manual or operating instructions. That might get you rotational position without having to measure phases. I'd bet there are some markings on the shaft/housing to ensure correct phasing. I also wonder if the xformers tie may be corroded. That would be easy to check by measuring resistance between neutrals.

If you go the transformer route to compare phases I'd caution you to be very careful. I don't think there will be a GFI and if so it won't quit until those 60 amp breakers trip. It could tingle a bit. I don't see any way to do it differently though if there are no markings to ensure correct phasing.