EDIT: This only seemed to fix the problem temporarily!
FOUND THE SOLUTION!
It seems it was an issue with the router.
My DHCP IP range was set to be 10.0.1.100-10.0.1.200.
This seemed to cause an issue with how the router handled the traffic between devices and would drop connections.
I set the DHCP range to 10.0.1.2-10.0.1.202 and it seems to work fine now....
I never made much progress trying to chase this down to determine the "root cause". However, for reasons unknown to me, the number of dropped SSH connections has decreased to near zero. The SSH software hasn't changed since I posted the question about 4 months ago... as of today:
$ ssh -V
OpenSSH_7.9p1 Raspbian-10+deb10u2, OpenSSL 1.1.1d 10 ...