js—I agree with your description of the situation. You don’t always want to bite the hand that feeds, but don’t want your firm to be needlessly exposed to unreasonable liabilities.
Sounds like maybe they're invoking some sort of contorted and misinterpreted ‘carnival-ride exemption.’ They may have the idea that, in effect, moving around country keeps themselves at arms length from building or fire inspections. If they are using unmodified lighting assembles interconnected per NEC, then article 410 [ie, showcase/fixture] may likely apply. If they’re using components removed from, or meant to be installed as replacement parts in fixtures, they could possibly work with an NRTL under contracts/agreements/conditions like that of electric sign builders. A ‘hypothetical’ call with the right person in UL or ETL [or ?] may be in order.