Thank you for your help, Matt.
That fixes the problem, but creates a new one: all reverse_proxy directives do not work anymore. Everything below file_server browse seems to be handled via try_files now.
:80 {
encode gzip
root * /Users/shared/server/components/web
file_server browse
reverse_proxy /soc/* 127.0.0.1:9710
reverse_proxy /api/* 127.0.0.1:9720
reverse_proxy /fio/* 127.0.0.1:9730
try_files {path} /index.html
}
If I remove the try_files line, everything works again except the rewrite.