I have the same scenario and agree with gardener that you can make small changes to the search parameters and sometimes get what you want. Consider looking for the target flights you want, then be sure you request flight times that specifically match your target flights. We also are allowed to pick a higher priced fare if we have a reason, like preferred departure or arrival time as well as non-stop vs connections. Saving $20 but having personnel unproductive for an extra 6 hrs per trip is not good business practice, so often I can book non-stops even though they are higher priced.

Welcome to the wonderful world of corporate booking tools. The illusory benefit to the company where they save money by getting rid of a corporate travel department gets completely washed away by traveling staff having to spend otherwise productve time searching and booking travel.