Forget VPNs, your problem is almost definitely buffer bloat. Google a buffer bloat test - bet you'll score F grade during gaming sessions. Your router's buffer filling up during gameplay = massive ping spikes. Enable SQM QoS if router supports it or get router that does

Over op's budget but the Optoma ML1080 runs off a USB-C powerbank, no outlet needed. 2.2 lbs, comes with its own carry bag. I've presented from places that had zero accessible wall sockets and it just worked. Denny's parking lot would be fine