Looks to me like it is the vise and alignment that takes the most time. I'd still use the drill press, but revise how each piece is clamped in. A vertical V corner, with a toggle clamp to hold the part tight into the corner maybe? Spend a little time making the jig so it can be clamped/bolted to the drill press table and won't move. Drop a part in, lever the clamp tight, drill the recess, release lever, then swap out parts to drill again.
What we don't know yet is how varied the parts are. Are they all the same length? Are they all the same diameter?
No matter the tool being used it'll be clamping/aligning the part under/over the bit that takes the most time. I don't recommend dropping a part onto a spinning router bit either. Clamping the part under a template is likely the best solution if the parts vary in length.
4D
What we don't know yet is how varied the parts are. Are they all the same length? Are they all the same diameter?
No matter the tool being used it'll be clamping/aligning the part under/over the bit that takes the most time. I don't recommend dropping a part onto a spinning router bit either. Clamping the part under a template is likely the best solution if the parts vary in length.
4D