Thanks everyone for letting me vent. I have never modified a reservation myself (other than Southwest). I have heard that changing an outbound flight is like booking a new flight all over again and I don't want to lose my inbound flight since that flight is very full.

I did do some poking around pretending to book a new reservation and the new fare was ridiculous expensive, which is why I wanted to talk to an agent.

My original RT was JFK to MLA via CDG, which I booked 6 weeks ago for $985. An opportunity came up in that I can spend a few days in Rome before getting to Malta. Who can refuse that?!
The new fare for multi-city route, JFK to FCO, FCO to MLA, and keeping the same inbound flight was $3,000!!!
I then tried a new fare for open-jaw JFK to FCO and keeping the same inbound flight and it was still $2,400! (This is silly since I can purchase the same one way directly from Air Malta for $86.)

Long story short, on my second call to 1-800-241-4141, after waiting an hour, the 1st agent picked up, only to have her "transfer" me to "international" and waited another hour until 2nd agent picked up. First thing I asked is if he's an international agent which he replied yes (phew! and I promptly insisted that he write down my phone number in case we got disconnected).

After explaining what I want changed, he quoted me a net change fee of $143.80 for changing to the open-jaw JFK to FCO outbound and keeping the same inbound!!! I have no idea why I was seeing difference of thousands of $ while he can do it with $143.80. (I was checking the new fares during the 2 hours wait time.) Of course I had him double check and triple check the itinerary. He even said the fare for this route is cheaper which is why the final charge is less than the $300 standard change fee.

I'm not sure if I had do this myself on the web I'd get the same low change fee since I never tried. I just know that new fare for the same booking online is literally thousands more during the time I waited.

Next time, I'll try the DIY method since it seems benign. 2 hours wait time is simply unacceptable.