Either record everything (with their permission of course) or just forget it and go old school.

These are professionals with additional training and a stricter code of ethics.

This "re-training" has been addressed above as well but giving them the perceived control of depositing at an institution always seems to make them comfortable.

We want to be fair but we also know not everyone trains their dog very well.

I also selfishly want use of the indoor aerial space for my own leisure and training.

Now, they probably shouldn't unless/until they go through training, but they are allowed to. 

It is non-linear, meaning that small homes have a much larger $/sf factor than larger.Yes, you should see a higher price for more acreage and a garage, but there are so many other factors to consider:Style, Age, Specs - location, condition, beds, baths, basement type, foundation type, sq ft, acres, local conditions like noise sources, flood zones, school zones, proximity to airports, gun ranges - that list goes on and on.

Your tenant has trained you well.When you have an illegal tenant in a unit, you can send the resident a lease violation notice stating that the person needs to be on the lease, and they can pay the application fee for the background check.  

The tenant works at a school and has great credit. 

It isn't a "war zone", but there is crime and the schools aren't well regarded.