I've heard a PAX request an upgrade on boarding (from Elite to Premium Laurel). The purser happily returned with a clipboard and credit card voucher for him to sign. When he saw the price he changed his mind - he was hoping for a discount but she could only offer it at a "standard" rate - which seemed to be the difference between what he paid and the full PL fare. I've known people to pay for upgrades at check-in at SGN and LHR - but again at a "standard" rate.

I've seen advertised cash offers at BKK check-in to downgrade or go with TG (this is London bound).

I've seen a sign at EVA's SGN office for upgrades on SGN-TPE-LAX routes on certain dates. Think it was US$75 for economy to deluxe (one way) - a real bargain. But not at the airport.

I used to get OP-UPed for free quite often from deluxe to business on the 747s between London and Taipei (especially on the BKK/TPE) leg. This happens less since the 777s were introduced, even though deluxe (now elite) is smaller and business is expanded.

So I can imagine if the flight is full and they are going to have to OP-UP some PAX, they might well take an offer of cash at a discounted rate... but advertising it is a different matter. Seems to me they risk incurring the wrath of the PAX who've obtained C class tickets at the normal price.

I've only been through LAX 4 times in my life. My suggestion to the OP is simply to make an offer based on what he thinks its worth. If the flight is full then they might take him up on it rather than give away an upgrade for free.