OK - I'm NOT doing any polyurethane - My better half is sensitive to smells...

Organic products, for the most part, she can stand. So (counterintuitive, I know) would it be feasible to wipe on glossy tung oil? I've used it on wood furniture without issue, so maybe on top of the vinyl as well? It forms its own surface, and when new oil is applied over the old, then it (like polyurethane) partially melts the previous surface to adhere.

Multiple thin coats might form a glossy finish (but without being able to soak into the surface, it might just stay tacky)?

The Rockler product might be the only feasible synthetic option provided it truly is "low odor."

My opinion is worth exactly what you're paying for it!