Thanks for the reply.  I read through both of those threads and the Debian bug report referenced in the latter thread.  Here's a little more detail on my situation:

I'm using only eth0 (well, and lo, of course), not wlan.

For essentially all practical purposes, I always have the network cable plugged in when I boot the Raspberry Pi.

I do not have Network Manager installed.

I boot to text console, not graphical login manager.

My directory /etc/network/interfaces.d is empty, and I have these four non-comment, non-empty lines in /etc/network/interfaces:

  auto lo
  iface lo inet loopback 
  auto eth0
  iface eth0 inet dhcp

Those four lines are identical to the corresponding lines in a 64-bit X86 machine that also runs Devuan Ascii.  The X86 machine does not have any delays.

Those four lines are also exactly how the datacenter network gurus where I work have always configured Debian-based systems for dynamic IP address on eth0.  Following the examples of said gurus, that's the way I have configured Debian-based systems I have worked with.  Except for cases whether the DHCP server (run by corporate IT) is slower than slow, I have not seen similar delays on those machines--only on the Raspberry Pi.

The X86 machine I mentioned and Raspberry Pi were tested with the same network cable, same port on the switch and router, etc.

When I boot the Raspberry Pi, the LEDs on the RJ45 jack behave curiously.  Initially, both are off.  Then, the yellow/amber LED on the right blinks on a couple of times and then goes back off--doing this once shortly before the DHCPDISCOVER line appears on the console and then again shortly after that line appears.  After the DHCPDISCOVER line appears on the console, and I think after the second round of yellow/amber blinks, the tree LED on the left comes on and stays on.

My hunch is there is something different about how the Raspberry Pi's NIC hardware, firmware, and/or drivers are initialized (relative to most X86 desktops and servers) that causes the initial dhclient process invoked by /etc/init.d/networking invoking "ifup -a" to fail/hang.

Is anyone acquainted well enough with the Raspberry Pi 3B+ NIC hardware/firmware/drivers to shed more light on why the Raspberry Pi shows the hang while the X86 machine does not?

I have a hypothesis that one possible workaround would be to remove the 'auto eth0' line from /etc/network/interfaces and add an "ifup eth0" or perhaps "ifup -a" command to /etc/rd.local.  Any second opinions on whether this would likely be reliable?

Yes, that would be helpful.  I'll be happy to provide that.  How many bytes from the start of the disk image are needed?  Does this BB have a mechanism to attach binary data--or--in what form should it be attached?

A couple of suggestions until somebody who really knows what they're talking about shows up:

1) Use "top" to see whether something is hogging the CPUs.

2) Use "vmstat 3" to see whether something is hogging disk bandwidth and to see what disk bandwidth you are getting.