I haven't encountered this quite so severely first-hand yet, but I'm wondering if it is possible/legal to provide a tenant with your email address only?

I have also encountered some very unpleasant responses to my direct mail letters.  

Had anyone encountered a situation where the renter acted more responsibly with their pet because they paid extra rent for the pet?  

I had it in my lease agreement "That  a tenant shall not park their vehicle(s) on the lawn or any other place on the property not designated as a parking area, or their vehicle will be towed at their expense"  and then saw they had a vehicle parked on the lawn or other area when I did a drive by, I'd take out my bright pink "Parking Violation" Sticker, stick it on the window of the car (under the windshield wiper) letting them know that they had 24 hours to remove the vehicle or the car will be towed.  

@Robert Friou those terms are significantly better than any competing product I've encountered.

You may be further limited if you encounter more mold.

Hope this helps.Regards,"Has any of you encountered an issue like this before?

You believing Zillow does 99% of the work for real estate agents means that either you've encountered really bad agents or you're not clued into what agents do.

Then I will have to raise rents more drastically, and everyone gets "sticker shock." 

Make up stickers with your phone number.