You can use a public subdomain like box.uuid.california.usa.mydns.org but we need something short like .l or .lan :) .home.arpa is terrible.

I have been using .l personally for a couple of years and it works fine except Chrome won't recognize it as a tld and would start a google search. Once it is visited a couple of times, it autocompletes it as a webpage so it's quite usable afterall.