Andrew,Whether or not you use the services of a Public Adjuster, there are a few things that can be done to prepare for what will be needed to settle your claim. 

She claimed she had paid the deposit; the previous owner had a different story and said that he had let her move in w/o paying one and never pursued it very hard after she moved in.

Someone who knows your business and who will be loyal due to the amount of work you provide, and can assist you with evictions as well as other matters (zoning, contracts, small claims suits, general advice, sending threatening letters to people you don't like, etc.).

At that time, my cousin (whose name is on the title), did a Quit Claim Deed to indicate that we all shared 25% each in the property.We are currently under contract at $285K and I'm interested in using the 1031 Exchange to defer taxes on my portion of the proceeds (approx. 25% which would be around $60K) Can I execute a 1031 Exchange if the title/deed is in my cousin's name?

Unless you could find another contractor to explicitly say the previous one was negligent, you're probably out of luck taking them to small claims court.

My hurdle however is that very time commitment and the "gamble" people who may not understand the investment often claim.

If you moved out in 2014, you might be able to still claim the 121 exception.Mark

There are no dog BREEDS excluded we have found that it is not the owner, it isn't breed it is most often an unusual situation that leads to a claim. 

Hence the reason for the research paper, which was started in an effort to explain to insurance companies that they are not underwriting  properly to reduce claims caused by canines. . 

Some risk-factors to consider: Small Lot, Top of the market, Not many Comps, Renting would be hard to cashflow+ with a mis-priced entry point.Is it unrealistic to have a max offer below $250k?