Sri Lankan here, who has flown on SriLankan Airlines umpteen times.

Historically, SriLankan Airlines has been pretty decent about date changes. I've done so several times (including on discount economy tickets), and have only had to pay a ~LKR 2,000 change fee + the fare difference between the dates (if present). Note that they've never had a "first change is free" policy (to the best of my knowledge), except for full-fare business class tickets.

Regarding your tickets - I'm not familiar with Sri Lankan's fare class codes, but based on what the staff quoted, my feel is that are of a special promo fare class, which does not allow date changes.

I suggest that you go to SriLankan Airlines' website, and use your PNR/Surname to view your booking. In that page, you should find a button called "Fare Conditions" (or something like that), which will bring up a popup with a bunch of plain text - the terms and conditions of carriage. The change fee (and whether changes are possible at all) should be listed there.

Unfortunately, SriLankan is facing severe financial difficulties these days; thus, even if its employees are sympathetic to your position, they are likely to have very little leeway to go beyond the terms and conditions of your ticket. As a worst case though, you could try dropping into their office in the World Trade Center and speaking to someone face to face.