Apples and oranges getting mixed together here. The ground school covers all arenas. ETOPS is covered. Hawaii is covered. Neither require a flight checkout. Cross reference chart, and CKA, both state that an ETOPS, or Hawaii flight, is not required before flying to Hawaii.
Without digging into manuals I think the logbooks have nothing(overland only), limited overwater(ie 162nm) or overwater.
We're using LUS procedures that leave us scratching our head so it cuts both ways.
Hawaii is ETOPS but the crew is not required to qualify (fly with CKA) into that division. NATS is ETOPS and requires a division checkout. No other division qualification allows the NATS qualification to be waived. Other division quals(ie NATS, Caribbean) do allow the Hawaii checkout to be waived.
MIA-SJU is not ETOPS. No ETOPS requirements. Without digging into the MEL I'd say the toughest MEL requirement ranking is - ETOPS/NATS, S. America, Caribbean and then domestic.