I solved this by replacing all links to ../subdomain.example.com with
./subdomain.acteon.net and moving the subdomain directories into the main
websites directory. I feel like there's probably some way to do this natively
but I just couldn't figure it out. If this is true and there's a better
solution I'd like to know.

$ cd ./www.example.com
$ find ./ -type f -exec sed -i -e
's/\.\.\/content\.example\.com/\.\/contnet\.example\.com/g' {} \;
$ find ./ -type f -exec sed -i -e
's/\.\.\/images\.example\.com/\.\/images\.example\.com/g' {} \;
$ mv ../*.example.com ./