If possible, I would move the stove, this would prevent grease splatter on your guest while cooking (ouch!)

It is my understanding that clauses disallowing sublease agreements don't prevent a tenant from hosting short term stays.Lease must specify that short term rentals are not approved.   

Him not being licensed may not prevent him filing a lien, and even if so, it would likely take you a long time to get to court to remove it.  

Could I upgrade my personal insurance to prevent this in the future?

Because of the Hurricane the Insurance companies will be imposing moritoriums on their agents preventing the writing of new business until the storm is past. 

Preventing that process is probably the greatest opportunity both for investors and victims.

Laws can be different in each state.Now is the time to seek advice from an experienced real estate attorney in your area to prevent any serious mistakes you might make dealing with these people.

Its not so much to be used as retaliation, but more-so as a preventative.

Katrina caused massive infrastructure damage that prevented people returning to there homes for months (not days or weeks, but months).  

That prevented me from getting a HELOC on my primary residence so I imagine it will come into play here.I'm looking for advice on next steps and timing.