There is zero chance of getting it done at the airport prior to departure of the first sector. The TA still controls the ticket until the first sector is flown

After the first sector, you can pay the AONEx differential (no discount for missing out on the sector). The only solution would be to modify the routing to have a short first sector, with a long transit or better yet a stopover, to give time to re-ticket after flying the first sector. Maybe upgrading to F isn't such a good idea for the OP's circumstances.