Here is what shows in the nginx error log inside nextcloud:
2016/11/18 12:40:17 [error] 304#0: *52 upstream timed out (110: Operation timed out) while reading response header from upstream, client: 172.17.0.1, server: _, request: "GET /index.php/apps/theming/styles?v=0 HTTP/1.1", upstream: "fastcgi://127.0.0.1:9000", host: "192.168.1.121:444"
2016/11/18 12:40:17 [error] 304#0: *53 upstream timed out (110: Operation timed out) while reading response header from upstream, client: 172.17.0.1, server: _, request: "GET /index.php/apps/theming/js/theming?v=0 HTTP/1.1", upstream: "fastcgi://127.0.0.1:9000", host: "192.168.1.121:444"
2016/11/18 12:41:27 [error] 304#0: *56 upstream timed out (110: Operation timed out) while reading response header from upstream, client: 172.17.0.1, server: _, request: "POST /index.php/login HTTP/1.1", upstream: "fastcgi://127.0.0.1:9000", host: "192.168.1.121:444"
As for switching from Apache, I may give that a go tonight, but if I can get it to work in Apache I'd prefer that.