Can't he just go to UK as a tourist, marry in UK and then apply for family/spouse visa?
That's one way which might raise eyebrows: he being American and her Polish they will put one and one together and figure out that he's trying to stay in the country longer.
He can enter the country but the fact remains he wants to live there longer with his partner.
Then again if he gets married here and apply straight away they will still treat it as suspicious.
I'm no expert but from what i know in such cases you just have to be honest.
U don't have to be afraid that u're not married to your partner at least they do recognise partnerships.
U say u have been together for two and a half years and have been on contracts in South Korea and Vietnam- show them all the proof that u have!
They are not going to refuse u the permit just because you have failed to produce some of the supporting evidence.
If they are not satisfied they can always call u up for an interview. After all you don't pay anything for the application.
PS: u won't be applying for a Visa but for an EEA family permit.