I agree with everyone you really aren't entitled, but with that said:

I assume you "paid" for F round trip in miles? So my way of thinking I would print out the miles taken out of my account and arm myself to show that I "bought" an F ticket, but am in C because they didn't have an F seat.

It would be a YMMV, but it does have some merit. I could certainly put together a good argument if it was me. But then you might spend longer arguing the merits of it and then waste more time than it is worth. But if you don't ask you won't get in either. Worst case you are in the RCC, or the ANA lounge which does have much better food than the RCC.