iMac Won't Restart, With Large External Encrypted Hard Drive Attached

I own three iMacs. (2009, 2010, 2015)

Each iMac has either one or two external hard drives attached to it, either by Firewire 400, Firewire 800, or USB 2. All external hard drives are encrypted (by Disk Utility). All internal hard drives are not encrypted. I use SuperDuper! to perform automatic daily scheduled backups from the internal boot hard drives, to their respective external hard drives.

All three iMacs experience the same problem during restart, approximately 50% of the time. The display becomes black. The arrow remains visible. The arrow will move, when I move the trackball. The arrow becomes large, when I move the trackball quickly, as it should. Otherwise, the iMac does not respond to either keyboard or trackball input. Each time that this occurs, I perform a hard power-off restart with the power button, which I don’t like to do. I have allowed the iMac to remain in this state for 72 hours, before performing a hard power-off restart with the power button. I can successfully connect to these iMacs, using VNC. The VNC screen is black. The arrow is visible. Otherwise, the iMac does not respond to input.

The following chronology of events details the start and occurrence of this problem:

2015-09-30 10.11 Install El Capitan

2014-10-16 The restart problem first occurred

2014-10-16 10.10 Install Yosemite

2013-10-22 10.9 Install Mavericks

2013-08-18 Encrypt all external volumes

The external hard drives are 1TB and 2TB capacities. All of them have approximately 75% of their capacities used.

Recently, I discovered that if I eject the external hard drives, prior to selecting restart, then, the iMacs restart normally. If I do not eject the external hard drives, prior to selecting restart, then, the problem occurs, approximately 50% of the time.

Recently, I erased the three internal hard drives, on the iMacs. I reinstalled OS X El Capitan, applications, and my user data, on all three iMacs. I erased all of the external hard drives. I selected journaling and encryption, on all of them, except for one. Then, I used SuperDuper! to create clone backups from the three internal hard drives to the respective external hard drives, except for the one that was not encrypted. This problem persists.

I disconnected all of the external hard drives from the three iMacs. I attached the newly erased, but empty, external hard drive, to one of the iMacs. I restarted that iMac with the newly erased empty external hard drive attached to it. The restart occurred normally. I repeated this ten times. No problem. I transferred this newly erased empty external hard drive to each of the other two iMacs, and, repeated the restart tens times each. No problem.

I erased this single external hard drive, again, with journaling and encryption selected. I repeated the previous exercise, on all three iMacs. Again, all thirty restarts occurred normally.

In summary:

All three iMacs experience this problem during restart, when an external encrypted hard drive that contains a lot of data, is connected to them.

All three iMacs never experience this problem during restart, when no external encrypted hard drives are connected to them.

All three iMacs never experience this problem during restart, when an external empty non-encrypted hard drive is connected to them.

All three iMacs never experience this problem during restart, when an external empty encrypted hard drive is connected to them.

Has anyone experienced this problem?

Thank you.