I've been running the numbers and trying to figure out my options. 1031 seems like a good choice, but finding replacement property would be very difficult.

Lisa,Good choice, @William Brown is absolutely correct.

This is also a topic of frequent discussion, I suggest you search the forum for related keywords and results will keep you busy reading for hours...As you read you will see who the real players are, do little due diligence, review their references and then contact 2 or 3 to speak directly, then make your choice.

If so that would be my first choice it can be processed fairly quickly. 

Because of our situation, we had no choice but to rely ENTIRELY on a PM.

I'd offer them the opportunity to have the lease amended to account for the pets (with pet rent) or the opportunity to break the lease and find somewhere else if they don't want to pay the rent.This gives them the choice and you a chance of not having to deal w/ turnover/eviction.

If you want lower your standards that’s your choice but be prepared for issues either with damage or non payment of rent and going through the process of eviction all while you’re collecting nothing and having to pay the expenses along with legal fees.

@Porter Nellans As a back up plan (aka one of the choices ) for your 1031 you can consider fractional ownership interest.

I have been studying different strategies and feel like I’m comfortable with my choice.

So both seem like a solid choice.