I would refund the difference. The "proper" way to go about it (at least where I work) is to attach the dummy itinerary of what it would cost if I followed company policy and what it did cost given my preference. Then when claiming reimbursement, I would list the dummy itinerary fare.

It's really no different than if you go on a company-sponsored trip and then decide to stopover somewhere incurring an additional cost (sometimes).

As far as being more "productive" since you were in first class, this is a purely subjective factor. After all, since booze is free in FC, what if you got smashed? I don't know how productive you would be.

Besides, if any company (and some do) believe flying in FC results in more productive employees, it would be company policy, period. It doesn't seem that way in the OP's case.

While $200 may not seem much, multiply that by dozens of trips by however many employees and at a certain point, it does affect the bottom line.