TA is correct in that if you revise your ticket before start of travel, it's a do-over. Although it probably doesn't apply in this case, until start of travel your TA 'owns' the ticket so you would have to use his services to make changes.

I haven't used CX for several years and airlines are competing in the race to the bottom in customer service, but they're probably as good as it gets (in OW anyway) for the moment. It appeared that like most airlines they didn't have a dedicated RTW desk (only AA AFAIK) so you're in the queue for general reservations. Their North American agents - the only ones I've used - were reasonably well trained in the product. If you have status presumably your call gets better service.

If it's convenient you can also have a ticket office sort it out for you although the changes will have to be priced and depending on how they do it, that may take up to a couple of days. AA's agents in the U.S. call a rate desk somewhere for this step, which can take days to respond. I recently booked and ticket an RTW by calling AA's South African agency, which got tired of waiting for the rate desk and did the calculation themselves. It's not rocket science; you can do it yourself with the help of ITA or some other source of the taxes-and-fees data.

As said, all the changes you make to your (already begun) trip at one time incur a USD125 charge, plus those taxes and fees. You can do almost anything that was possible when you first ticketed, with those same fares and rules continuing in effect.

I think some airlines may help themselves to a 'convenience' fee on top of the $125, but maybe that's just me being cynical - I can't quote an instance.

When requesting changes it's probably most efficient of everyone's time if you've already selected the flights you want and have verified availability in your class of service.