First thing you need to tell them to do is put in writing that they would like to break the lease and then you can begin marketing for a new tenant and try to mitigate their responsibility.   

He did the mitigation for us and I like him. 

This is your best risk mitigation

Risk Management: What strategies or considerations have you found effective in mitigating the risks associated with high HOA fees?

Also, look into the policy details as I've seen some insurance companies that don't want to cover you on a rental if you rent to students (in Madison, WI students are a protected class you can't discriminate against in at least considering as a tenant, which I mentioned to this insurance company, and their simple response was that they can underwrite policies however they want in mitigating risks).  

Does anyone with more experience have any advice on how to best mitigate a HUGE loss here?

This is why a random REO sale does not blow-up everyones value's, because appraisers take that mitigating fact into account. 

The law requires that you make a reasonable attempt to re-rent it to mitigate your losses. 

Still trying to get data about how difficult it is to get your kids into the good school, and how expensive it would be to mitigate downside school risk by going private for 1-X years (could get expensive if BOTH are in private!!!) 

I was planning on hiring a property management company to interact with the tenants specifically to mitigate liability.