I tried excluding the entire Adobe directory, but that didn't help. It is definitely a Firewall issue, I can leave the rest of the shields on and it works fine.
So what I eventually found were the firewall rules in Avast. There are many auto-created rules that allow things through, but they weren't letting these apps make the contact they needed to run. Avast has a setting that allows you to let it 'auto-decide' on the access for any apps where the rules don't allow some type of communication. It works for the most part, but I changed all of the Adobe apps to 'ask me' (some 70 or so entries!). Then when opening Photoshop, it asked for permission for several services including dynamiclinkmanager and qt32server. And the same happened for Media Encoder and Premiere Pro, except they each asked for access for their own self-named host program as well. Now they open without issue. So I'll leave this here for others who may run into this.
As a side note, I saw the system trying to use port 2869 in the firewall logs and added an exception for it, but that didn't help. But the above solved it, at least for now.