Yes you've done well. You will never avoid those disruptions altogether unfortunately, and of course the risk is multiplied if you insist on taking lots of connections for the extra tier points. The best an agent can do, I imagine, is perhaps take care of the problems in the background while you get some rest at the hotel. But usually the airport agents have substantially more flexibility in rerouting you anyway.

As for the FFP, well it's your company and if part of your motivation for you as a director and perhaps for your employees is FF perks (at appropriate prices), it can hardly be a unique proposition—albeit one with fewer and fewer subscribers these days (are you hiring? ).

If I were in your shoes, I'd draft a simple list of requirements for the travel agent [actually a proper travel agent! with access to a GDS, can issue tickets and so on; access to bulk/discount fares which earn points on BA; familiar with BA Executive Club; familiar with the BA On Business programme; understanding of oneworld and other alliances and that not all fares earn on BA; ability to process UuA; able to do Reservation Assurance; repeat the same with other airlines you use; the same with your preferred hotel programme]. Then I'd circulate that around the major providers and google a few smaller providers, perhaps even independents near you in need of a reliable customer. And see what comes back.

I'd be interested to hear how it goes if you do go down this route.