but our Dev Director won't approve it till it's been tested.
Until DNS solution over a hosts file has been tested? Tell your Director to read the history of the Internet. DNS (BIND) was invented because managing hosts files became unmanageable over multiple hosts. Do they have a particular hang up or question that we might be able to help address? DNS was designed for this very purpose.
In the mean time, I might suggest putting the master host file in a centralized location and then creating a cron task to synchronize among the various hosts. SCP would work, as would rsync. By setting it up as a cron task, you would guarantee that updates were propagated regularly. Given the what I presume to be the limited (small) size of the hosts file, you could even have it synchronize often without ill effect to your network.