If you book through a corporate TA, it may well be that the TA "sees" every change to tickets it issues, even if you pay for the changes and that those changes are reported on some report to your employer. It may also be that your employer could care less and does nothing with the report and looks only at what it pays.

Same thing if you pay for the ticket and are reimbursed for it.

Thus, we need to know what your employer cares about it. Is it that the employer only pays for ET or that you actually fly in ET. Does your employer really care that you fly in CE so long as it pays for and you can document the cost of ET?

Answers to these questions would allow us to help you a great deal more.