Delta does file cheaper fares through certain websites as (1) part of Amex IAP if you have a platinum card or (2) as part of package deals where you book a flight and hotel/car reservation together. The package deals will often earn as exception fares too.
Sorry I was imprecise, when I referred to "sites", as the OP did, I was referring to publicly available sites to purchase flights from, not membership programs or packages, particularly since the OP already has purchased a cruise. Some people think the same flight will be cheaper on booking.com versus expedia etc. That is not generally the case. I was not speaking about access to special rates not available to the public. Some rates are cheaper if you book for US federal government travel, etc.