I'm not an expert on the technical issues here, but I'd add that DL usually charges a fee of about $50 to take over (before the day of departure) a ticket that was issued by a travel agent. Your employer could have resisted reimbursing this fee as in principle you should have contracted the travel agent to fix the problem. OTOH, if the timing of the trip was important, hopefully the employer would understand your concern and decision to take the initiative and solve the problem since your corporate travel agent didn't seem to be doing anything here. I'd agree with the suggestion to fire the travel agent.

There are minimum connecting times (MCTs) established for connections (on the same ticket/PNR) at major airports, depending somewhat on the carrier(s) and nature of the route. If MCT is violated, you have an illegal connection and the ticket shouldn't be sold/issued; check in (or bag check) should not be permitted if a schedule change (not an ordinary minor delay) causes MCT to be violated. The idea is that if you miss such legal connections, the delivering carrier that had the delay is responsible for rebooking you for free.