A change of route does require a ticket reissue. If you don't change the first segment you should not lose the pre-April 15 rules, however, the agent/airline could be viewing this as a cancel and new purchase in which case you'd be subject to the current rules. This is a matter of interpretation and, as Darren recently reminded us, regardless of what the rules say, you are stuck with the way the person issuing the ticket chooses to interpret them.

As far as open segments, your T/A is just wrong. There is nothing in the rules specifically allowing or denying this so, again, you are stuck with the way the person issuing the ticket chooses to determine the rules. Specifying segments isn't going to hurt you but might cause a hassle later on when you want to change them. The rules do specifically allow time/date/carrier changes without charge (or ticket reissue).

If you want to pursue this further, you should find out what airline the T/A is using to issue the ticket and contact that airline's RTW desk to discuss these matters with them directly.