I think I got it all sorted out.  The introduction of the new modem/router seems to have triggered the network of each machine to be set to a Public network, rather than a Home one.  I reconfigured it, and I think it's now working.

I have to see if I still have the issue of Multiplicity frequently disconnecting from one of the secondary PCs (and then quickly reconnecting).  But at least it's working as before.

Ya, I always use direct ethernet, not wifi.

Got it sorted out, like I said.

I do find that sometimes Multiplicity windows seem to disappear (not visible on desktop, and no minimized icon on taskbar), and can only be brought back via Task Manager.  I had one odd error window pop up one time, as well.  I took a screengrab, and will have to post that here sometime.