You are trying to change not one, but two rules.

1) As discussed above, SDC and SDS are only allowed on international tickets after all international portions have been flown.

2) Award tickets cannot be changed and reissued within 72 hours of flight time.
(Although that does contradict the SDC rules!).

It seems unlikely that you can override both of those rules; I'm surprised the DL agent even offered you the option of an additional 60,000 miles/person to change the tickets.

On the page you've shown it doesn't say international but at the top it does specify US, Canada, Puerto Rico, and the US Virgin Island as the destinations where you can use SDC and SDS.