I would like to keep it but it's difficult to separate how I feel emotionally about the property and what would be more financially advantageous. 

You need to place temporary supports to do this work. 

Very hard, the best way for you would probably be a student visa but thats only temporary.

You did so when you were not emotionally involved.

My number one advice getting started is to not make emotional decisions EVER.... run your numbers.... don't trust them?

Often times we get emotionally over-optimistic about a particular property and we lose sight of the potential downside.I'm not sure if youve ever heard of a Monte Carlo simulation, but what that does is take your projected numbers and runs them through a predetermined number of simulations, sometimes over 1 million different scenarios if you wanted it to.

If my tenant claims the pit as an emotional support animal, do I have to allow them or can I legally deny based solely on breed?

Yeah, I plan to take the emotions out of it, run the numbers, and stick to my goals. 

When looking for a primary residence it was much harder to detach emotions from the mix.

Just like any court "settlement", the decision has to based on the numbers...not emotion.....unless you are willing to pay for the emotional satisfaction, which is your choice.If it cost you $500 to get them out in a week vs $1500 to get them out in 30 days...... the only justification to go the 30 day route is the satisfaction of having the eviction be on their record and giving the next landlord the heads up....which I fully support....and the possibility that you avoid getting the reputation as a pushover (which can be dealt with by properly screening your next tenants)......but from a financial aspect it doesn't make sense.So you may see a lot of people on here chant the mantra of "run it like a business....no emotion"..... but then in this situation, make financial decisions based on emotion.