So sorry for the slow response. I'm not aware of any slowdown that should happen while you're playing on the LAN 3rd wave, but I haven't updated the itch.io app in a while. Really glad you're enjoying it with your family! Your machine looks plenty beefy enough to host. Although I will note that the server does most of the heavy lifting so you'll definitely want that to be your beefiest machine.
I'm not sure I can send you a DM in itch, but if you join the discord or shoot an email to info@pluckyrat.com I'm happy to shoot you an alpha key (or a few) on steam for you to test the latest version.
Thanks!