Constantly moving is tough.
Really you need auto load, and auto unload to make that happen.
I don't have that, so we have the parts carts as close as reasonable to the router so the distance is as short as possible when racking them.
Average cycle time for us is about 12 minutes. That's from hitting go button, to hitting go button.
So start, machine, unload, load, hit start. I'd wager 5-6 minutes of that is labeling with a sharpie and unloading, blowing off the table, and pulling the next sheet on. That can vary wildly, we have a tiny 4 drill, drill block so if there's a ton of shelf pin holes, it adds a bunch of time.
Time spent while the program is running is usually getting the next file queued up, dealing with the waste/drops from the previous program, and studying the parts listed on the current program's nest to facilitate faster labeling.
I don't run enough sheets a week to justify the cost of the floor space for auto unload. It'd be nice, but I just don't have a need.
How many sheets a day are you running through two cnc's? What's your average sheet time? I ask because if you're doing 80+ sheets a day, that'd 3 people in a hurry I feel.
As far as pocket holes being faster, it's not. It does save handling, and less potential for them being forgotten. Plus you can put them in places you can't reach with a Caste Machine. It does work well. The pilot holes can be an issue in MDF I've found. It'll split the material. Plywood doesn't seem to be an issue though. I don't do much particle board, so I can't say how it works there.
It's kinda like boring holes for hinges. The boring machine is faster because you're punching 3 holes at once, but the cnc doesn't make mistakes (The moron in the office maybe....), and you don't have to touch them another time.