There is currently no way to check for F inventory availability on CO.

Your best bet is to do OLCI as early as possible. The chance of an F seat opening up between then and the 3-hr mark (when all remaining seats are typically cleared for upgrades), and a lower-level elite checking in just at the right time to snag it are pretty low. And even if it did happen, you'd have little to no way to "beat" that other guy, since it's purely based on luck as, like I said, there is no way for the public to identify when F inventory opens.