Surprised they had to hand-write the whole thing.

They should be able to simply mirror the other segments in your first PNR and check the bags straight through. This would also be preferred because if your connection is delayed, they may better be able to help you out.

Do this all the time with multiple same-airline tickets, and more often with tickets of alliance partners or other airlines where an interline baggage agreement is extant. From CO to CO should be a no-brainer.