I tend to doubt you'd be able to negotiate very far with the gate agent. Negotiation is rare in consumer-business transactions in the US, and in the few cases where it is normal practice, consumers absolutely loathe it (generally because there's no real "negotiation" going on anyway, I guess). Americans don't like to barter, they just like things automatically as favorable as possible, and I'd be surprised if your gate agents have any authority to do anything other than follow a three-step simple elevation process like: "Will you take $50? $100? $200?" If high number is rejected, the agent is probably obliged to move on.
This is not really negotiation, but a scripted process of elevation that some know how to exploit for maximum benefit and some don't.
It is usually done as a uniform price auction, with the airline upping the offer until they have enough volunteers. All volunteers usually receive the same (best) compensation regardless of what level they first agree to give up their seat. At least in my experience, you are right that it is not possible to negotiate directly with a gate agent, but then again I'm sure those with superior negotiating skill can negotiate just about anything.
This is not really negotiation, but a scripted process of elevation that some know how to exploit for maximum benefit and some don't.