Odd. My new 3800 printer has a similar "pump" sound: every 4 passes of the print head, I heard a groaning noise. Tech support said it was the pump, and normal. (They listened to the sound thru my phone!)
I just received my second replacement 3800 ( yeah, I'm on my third printer) but this one is a keeper.
I can tell you right now, from what you describe, this is not normal behavior, in fact, your pump is running about 4 times more than mine did.
After loading all of the inks and pressurizing all of them, I heard the pump make ONLY one cycle, and that was after I ran a nozzle check, as well as two 11x8.5 prints and one 25x17. This single pump cycle happened two hours after it pressurized the inks, and was half way through the last BIG print.
After turning the printer off, you can hear it dump the air, which is something I didn't hear on my last defective printer.
If I were you, I'd be on the phone with Epson, and tell them this is not normal behavior.
All I can say is, thanks Epson for standing behind your product.