Wouldn't the bank want to rid itself of it?  

I have 2 unfortunate mortgages against my home I should never have taken out, (borrowed to invest in rental property) now with very very low income from rents only and no job, I am afraid of not being able to have a free and clear home anymore, my goal is to get rid of those 2 mortgages as I cannot afford them but I have 2 free and clear rentals that I have owned for 9 years.  

If it's not prescribed and you explicitly stated in the lease agreement that they were only allowed 1 pet in the property, that's when you have more options like telling them they're in breach of the lease and having them resolve the issue by getting rid of one of the pets or complying to any additional pet fees you may have.

I have never had any luck convincing smokers to stop smoking in their rented apartment or home.What that in mind, I would not use the term "smoke-free" within their hearing until I wanted to get rid of them.Full disclosure: it took me four hard years followed by an ultimatum from my then-girlfriend, now-wife to quit smoking for good.

I would get rid of it and not make that mistake again.

I want to get an estimate of the increase in value for two reasons, 1) to refinance out of the FHA loan, and/or 2) to cash out refinance/get rid of my MIP.

I will sell the rental when the lease is up, less than  a year, then I can pay the HELOC or reinvest but really really want to get rid of this adjustable, Im being financially waterboarded.

I wouldn't do too much demo or get rid of the appliances until you're sure how far your budget will go.  

If it comes back poorly, then we could be stuck holding some of this debt and having to figure out a way to get rid of it in a different fashion.

I'm looking for a reason to get rid of them and lying about income on an application is a reason to evict.