UA can take over a ticket that’s been booked by an agency; there’s a $50 fee for this. I’m not 100% certain whether or not they’d be willing to do that in this case, but it wouldn’t hurt to ask.

Chase’s options are limited by the fare rules. On many of its nonrefundable fares, UA has written language into the rules that fare differences are ignored (i.e., not refunded or credited) if the price drops. It then ignores those rules and gives credit anyway, but only for tickets that it issued (or was willing to take over). So, if your fare is non-refundable — which is going to be the case if either your outbound or your return is non-refundable — then, unfortunately, Chase probably can’t give you credit. I don’t see any $6600 fares coming up, but I checked an $8700 fare for the end of August, and it was a combination of a refundable B fare and a non-refundable S fare… so it would not be refundable, and this rule would apply. It’s an extreme disadvantage of working with a travel agent, and it’s quite unfortunate.