It depends on the situation, but yes if you are making offers low enough that 90% of them will not be in contention, and you are asking for bids on every one contractors will get fed up with you real fast. 

And if so, how does that work in this situation? 

On the podcasts, the term refinance is used frequently but I am not sure how it applies to this situation.

Of course, there are exceptions to the rules below and every situation will look different at every turn.

For what properties and situations it is most useful. 

premium for A1 service, in certain situations.

Perhaps you had a situation in the past where you did not pay a bill.

Outside either of those two things you really better hope the stars align in your favor in court and have an absolute airtight lease that backs up your actions.I'd issue the 30 day notice (be civil, no need to further deteriorate the situation with hostility even if you would prefer to kill them...) and make the primary goal to just get your property back. 

What resources do I have in this situation? 

One of the times I attempted to bring up this situation, they told me that they don’t even let their child into the backyard since the dogs are so territorial (sounds like fun when they break down the fence). 2) I am trying to determine if I should sell or rent my house.