I didn't realize how complicated it would be to work things out. I'm already missing the days of just buying on a personal card and getting reimbursed.

I finally got a hold of our corp TA and they couldn't explain why a coach ticket would impact the price of F fares. I did go ahead and book through them and buy up to F (I had already confirmed that nobody would get pissy about this in the travel department). It turns out that the coach ticket went up enough to make the difference between the F fare the same as before the jump.