Thanks Pie Lover,
I guess I have not been clear enough about my USB setup and peripherals. I have 3 USB hubs of different ages and capabilities to accommodate a large number of peripheral devices, 3 printers, a scanner, a smart battery backup unit, etc. Because some of these slow-data rate devices are a considerable distance (8-10 ft) from the computer I have an 8-port USB 2.0 hub that accommodates these and this hub has its own external power supply. This has a long USB cable that comes back to the close vicinity of the computer and plugs into a USB 3 hub, see below.
Closer to the computer are still more peripheral devices that are not particularly demanding of high data rates, but are a mix of USB 2.0 and 3 devices. These are serviced by a 7-port, externally powered USB 3 hub that is plugged into the Mini via a USB port on the Mini. The 8-port "slow" hub is daisy-chained into that "close" hub as I said above.
A second close hub is plugged-into one of the two Thunderbolt ports and it is nearly crippled with respect to its USB 3 ports - they work sometimes but mostly don't. The TB hub has other ports for SD card, HDMI, etc, but I have not tested them as I have been preoccupied by the USB issues.
Finally, the second Mini TB port is used by external HD box, the Mercury Elite. The Mercury Elite box is not interfaced to the Mini via a hub (ugh!) but rather it is direct to a TB port - that's the only way to get decent disk transfer speeds.
I just added a 4TB Toshiba HD to the Mercury box a few days ago and that's about when boot times began to stretch-out. Unfortunately, I did some other changes about the same time that may have had some effects on boot time issues. I used an SSD in the Mercury box to build an external clone of my internal SSD to be used as an emergency backup boot device and I test-booted from that external SSD. It worked and while it was a slow boot, I was not then aware of the external non-Apple SSD Boot issue and just noted that it was an annoyance to look into later. ***Under all other conditions (I.e., when not needed for an emergency boot = virtually never) I always boot from my internal SSD.*** Thus, according to my further reading of other's troubles with long boot times **when booting from non-Apple external SSDs,** my situation does not seem to fit their conditions.
To make things *more* confusing, last night I ejected the external SSD from my desktop (i.e., unmounted that disk - just to see if having on the desktop was somehow a problem) and, voila, this AM the Mini booted very quickly, even though, as expected, the external SSD re-mounted along with all of the disks in the Mercury box. I will do more testing to see if this "good behavior" persists. And also , as expected, there was no change in the USB situation (why would there be? - I'm just grasping at straws, here).