Are you paying for the scheduled pickups? If so, I can't really see how they can complain. The logistics are their problem, not yours.
In general, if you do around 15-20 boxes of that size, and tell them its ok to come at the end of the day after all the deliveries, it probably should be ok. I had some issues a few years back with time of pickups, but once I told them I didn't care if they came in the evening, it smoothed over.
I've had pickups several days in a row without issue. I of course it's very YMMV depending on whom you are dealing with. I had the worst experience at a UPS store one time because the owner was a jerk.