So I tried running the Push Deployment Wizard and I ran into an issue. The server couldn't see the Computers on the network, complaining that the "Computer Browser" service needs to be enabled.
I checked it out, and somehow, the "Computer Browser" service was "disabled". I re-enabled it back on and started it back. The Push Deployment Wizrd still didn't load the list of computers, but it attempts to (loading/hourglass shows up).
I started the SEPM Console again and did the Client Deployment Wizard again. Browse Network>Microsoft Windows Network (it will load/scan) and only the top level forest domain controllers and forest servers are visible at the moment... At least this has gotten me somewhere, where this wasn't even loading at all. Through Windows Explorer, I can see all the machines (top forest, and child domains). It seems like it's taking a while for SEPM and the Computer Browser service to go through all the machines in the whole domain. So, it looks like it was this service being disabled causing the browsing network issue, although, the list isn't populated with all the machines I used to see a few weeks ago.