OK... I *FINALLY* got this working! First off, that ScreenBeam didn't work at all. It actually requires a receiver which plugs into an HDMI port like a TV or Monitor. Totally not what I want to do here.
I got this working by the time-honored, traditional, good ol' fashioned rebooting of machines. I had to reboot both my workstation PC and my Surface Pro. I also removed the
WiFi usb adapter before doing so.
After both machines rebooted, I first went into the Surface Pro -> Connect (lower right settings action center) -> Projecting to this PC, and set the first dropdown to "Available everywhere". What this does is create a new WiFi network adapter if you look in your network connections.
I then inserted the WiFi usb adapter into my workstation, connected to my local network, and went to its Connect in the lower right settings (action center), where it began to search for my Surface.
In the past attempts I tried this, nothing appeared. But this time I got the Surface Pro and other devices on my network that the Surface Pro sees.
So, in short, rebooting solved this problem. I should have thought of that sooner.
ALSO... and this is a total headscratcher and incredibly infuriating... but, I took out the WiFi usb adapter to return it to the machine that it was installed on,
and my display was still active on the Surface Pro! So, it appears it requires a WiFi to connect to the device, but then it does
establish a connection through the wire if it exists. icanteven with that!!!
Hopefully this will help someone out there with a similiar situation.