So if you're moving back strictly for taxes - you may need to reconsider, after running your numbers with a competent accountant.If you had a good excuse to move out after 15 months - like a job change, family change, health change etc. - you may be eligible for an exemption already.So, before worrying about proving your residence, make sure that your tax plan works.

I would suggest removing all four, and temporarily replace with basic, inexpensive, battery operated units.

I just came across this: http://www.phila.gov/health/childhoodlead/LeadPain... which states that in Philadelphia, PA we if we're renting to children aged 6 or younger we actually need to have our properties certified as lead paint or lead free.

I'm losing a great tenant because of this neighbor, & I'm afraid of this situation happening again if I re-rent.I suspect the neighbor has a mental health issue. 

The batteries end up costing more than the device though  

Everything sounds so good until battery dies.

According to the Tenant Landlord Act if there is a health concern the rent would have to be abated, meaning that the tenant has to move out until it is repaired and does not have to pay rent.What if you didn't have patio screens?

One of those inherited tenants opened it (which anyone can do- changing battery, etc.) and crossed the wires so that the boiler would go continuously.

This works like a cash out refi loan but its really a purchase loan.For all three options above :- Buying in the name of an LLC adds an additional issue or risk (Its a new rule and not applicable to me so check into it with your broker)- Condos and HOAs could prevent approvals if the health of the HOA is questionable or if there are several Rentals in the community already, existing lawsuits, budget concerns, or too many units owned by the same entity. - Ask your mortgage broker to verify your refi plan before you go ahead and buy anything you plan to refi.  

I agree with @Ronald Rohde, it sounds like simple battery Schlage keypad deadbolt locks would be a good fit.