So call the airline then if you don't want the 'high' fees.

By ringing up a TA, they can see immeidately where the better booking class is and how to circumvent the booking to make that seat available. People with CRS access may think that they know what to do , but even me with 20 years experience still scream when that LAST seat is gone before I can end your transaction in time just because the airlines' computer don't like what you're doing with the booking. A TA may do that for you. Offer alternate flights connecting to different airport. or one that leaves an hour later than your preferred flight, or earlier.

An airline res agent may not be able to do that for you.