Using a compass & chain (tape).

Wondering if I should terminate their month to month and stand firm on my offer of $625/mo and them paying the water bill or if I should exercise some compassion and take a little less to avoid a vacancy.

I do not have the faith of a priest in Christ in the moral compasses of the top private finance professionals of the USA.

I run my business with a lot of compassion and I pride myself on working hard and being easily available.  

That is a testament to your property management skills coupled with a sense of compassion.

Sorry you are dealing with this.I admire your compassion for the tenant, but I would not want to continue renting to someone who is hoarding and won't let anyone in to perform maintenance.

My family and I also regularly serve at 2 different shelters in my city, and 10% of my company's profits go towards helping the most impoverished people/communities in the world through Compassion International. 

First, out of compassion.  

PS- I've heard the BBVA Compass Bank has a 0% down owner occupied program now.

Showing compassion goes a long way and they might see you in a new light and do extra things to take care of the property or not bother you with issues with the property anymore.