I priced it out manually in the Sabre GDS.

There is no codeshare on this route / for this city pair, so you'd have to book this journey with a DL flight number and then the AS flight number. This combination of flights will not price at almost all of the lower Economy fares per those fare rules.

However it looks like you're planning to book a First Class fare.

This is different as the lowest First Class fare for these city pairs for a random date next week (P fare) is actually slightly lower if you mix/match the carriers. For the fare of $374 - you can fly on DL or AS or a mix thereof for the same price. Ironically, this is actually lower than buying it all on DL metal ($386 one way in P).