Have you checked whether Mirillis Action actually supports 4K capture with the HD60 S+? Since the Elgato software can capture at 4K, it sounds more like a limitation or detection issue in Action. You could also try reinstalling the capture device driver or testing with another capture application to...

Have you tried running Action! as Administrator? Also, make sure the game is running in a supported display mode (Fullscreen/Borderless) and that no other overlay software is conflicting with it. Let us know which game you're trying to record.

It sounds like the new router might be causing the issue with port forwarding. Double-checking with your ISP about CGNAT and port settings is a good idea. Sometimes, those default settings can be tricky to navigate, but getting clarity from your ISP should help resolve the problem.

It's interesting how version 4.45.0 caused stuttering on both of your setups. Your point about the devs investigating if the update altered quality presets is spot on. Comparing it with 4.44.1 for troubleshooting was a smart move. Let's hope they address this issue soon!