Re: You're not using MySQL's built-in replication???
"...would take a matter of days before they demanded that production workloads started operating off of it."
You bill it as a "backup." They wouldn't, rightly, demand to run your backup copies of the network shares as a production datastore, so they should not demand a backup DB to be a production workload. It is the network admin's job to teach that.
For TPTB for automated switchover: your example of why auto failover is a Bad Thing in your case should be the exact argument against doing so. As an admin, there's a fine line to walk between "I can make it do that" and "that simply can't [shouldn't] be done." IT is as much an advisory source as it is an enabler. Just because I can set up a group of FreeNAS boxes as iSCSI targets so I can scale up my environment to 60TB doesn't mean I should, simply because TPTB demand more space, but won't pay for a SAN. Likewise, caving to each want and whim of TPTB that don't allocate proper funding to do it right (or at least "better"), is not correct. Of course, with their software, there's not much of an "ideal" way to do it. Manual failover, manual corrections in the event of DR, etc. It's just how it is, and TPTB need to understand that.