I knew perfectly well that Ethernet goes up to 1000 megabit/sec and WiFi generally 50-200 megabit/sec, but my reasoning was that the LAN shouldn't matter because my ISP only gives us ~6 megabytes/sec (or ~45 megabit/sec) and as far as I knew, all possible configurations easily saturated that as my laptop and repeater were the only things on WiFi with no interference from neighbors. In performance, you usually focus on the weakest link, and here the weakest link (ISP/Internet) was by far weaker than the other links.

Apparently I was grossly wrong, and I still don't understand why I was wrong and why the changes made such a large difference. Something to do with network protocols and response to packet loss or something, I guess.