Cassius19, since I don't know the exact get it done details of your office, I'll just tell you what we do in our office.

We also do not make the actual flight arraingments, we have a travel coordinator for that now.
But we do have the ability to research potential flights and request that departure/arrival be at certain times. Why? Well, you know... because our customers choose the mtg times and we have to follow the whim of the customer!
We can't help it if the customer requests a 8am meeting so we have to arrive the day before. And we also want to arrive early enough the day before to be able to get to our hotel and have dinner and relax (or prepare for the mtg) so we are not stressed out.
Or maybe you like to not leave your home (family or cat or plants) until the last minute, so you are not away from them any more then you have to be.

For example, I need to be in BOS on July 15th sometime for a meeting on the 16th in the morning. I just let the travel coordinator know the exact time I need to leave on the 15th, like 2:30pm. Oh, what... a NW flight happens to be leaving at 2:30pm, how convenient since my carrier of choice is NW.
Granted, the price needs to be reasonably close to any other flights around that time. (It helps that DTW is a NW hub as well).

The Travel coordinator also has us fill out a "traveller profile" with our carrier and hotel preferences, FF info, etc. Maybe you could suggest that for your business as a helpful solution to help whoever is now making the travel arraingments.

Good luck and I hope you figure out a way to keep earning the miles you need!