As a wholesaler, I would think you would only make so many different sizes of drawers. Would you not have a list of standard lengths to cut? 300 boxes a month is only 15 per day. That is 60 parts, and if cutting 2 at a time, that is only 30 short cuts a day (not including trim cuts). If you can cut two pair at a time, then you are making only 15 cuts per day. I would be inclined to use flip stops and stop blocks first on different saws to figure out the best sizing method for you. I would not be inclined to pursue automation until making 50 - 60 boxes per day, with a proven cutting method.
FWIW, I used a Striebig without scoring with a regular stop and a flip stop to stack cut (up to 4 at a time) vinyl drawer blanks. The flip stop was to cut my shorter standard box sides. Fairly safe, but I learned to cut the short lengths first from my optimization. Downside to the vertical is the shelf is short. If not careful, the blanks could twist and fall off the shelf sometimes. If you used a dedicated machine for this, the operator would learn pretty quick how to avoid doing so.
In order of my preference, I have cut a lot drawer blanks on a Striebig without scoring, a radial arm saw with scoring, and a scoring table saw with a sliding carriage.