Clever trick! And I was obviously wrong.
There has been a similar report, not with 4TB drives, if I remember correctly, but with new blank disk.
Pitty that you don't have a kernel and hotplug log when the disk was not recognized, as that could help.
Disks are detected by the linux kernel, which generates an hotplug event that Alt-F uses, so the question is to know if the drive was detected by the kernel or not and if the event was generated or not.
Although its name is "hotplug event", it is generated also at boot time.
I guess that you didn't try to hot-plug the disks in the right bay with power on? It is possible, and I do it often.
If the issue was related by a long disk spin-up time (big disks are slower to start), could that "confuse" the kernel?
Some disks, specially rack-mountable SCSI disks, have a jumper to delay boot at power-up, so that several disks powering-up simultaneously would not put too much stress on the power supply.
But no, that does not explains why the disk becomes recognizable after it was formated, so the issue has to be related with new, blank, (big capacity?) disks.
Thanks for reporting back the cure.