With the training required to meet skills test standards and the requirement for a skills test too, I think the flights would have to be conducted from a licenced field.
I disagree.
Inclusion,
Renewal, and
Revalidation of a rating are distinct concepts. If the pilot has ever held an SEP class rating, this is a renewal (LASORS makes this explicit), and any training does not require a licensed airfield. Note however that the Skills Test does require a licensed airfield.