But, if you can afford it, I'd put a little fridge in each unit and a microwave, and maybe even a little coffee maker, to lessen the traffic in the kitchen.  

You know, since that guy is acting like he has the right to go do what he wants on your property, what you might do instead of putting up signs, is send a letter to the adjoining property owners, just saying you've bought the property and want to stop the foot traffic through it, and here's your contact information, and please let them know if anyone goes onto the property, as someone's been vandalizing your plants.  

I agree that permanent flooring in rentals is an issue in big traffic areas.

For the rest, I'd make an appointment for them to see the unit, letting them know that the first approved tenant who actually signed a contract and paid the security deposit got the apartment  & that I kept showing the unit until that is what I had.And if they were late (without a call with a dang good reason like they're stuck in bumper to bumper traffic, which I could verify on Google maps) or didn't show, they were denied.  

It's on a high traffic road and across the street from an expressway.

It took the plumber 15 minutes...but saved me two hours in traffic.

No "pattern" of trouble with the law.  3 or more misdemenaors (except traffic tickets) in 5 years or less is NO GO. 

They are also doing many other roadway projects to allow for increased traffic around the city.  

They'd have to normally go to work, possibly have to work late, get stuck in traffic, pick up kids, etc., and remember to get a check to you wherever that would have to happen.Just don't set them up to fail, is my advice.  

Have your criteria in writing and maybe email it to yourself, so you can establish a date for when it was created.I also denied anyone who was late for an appointment with me and didn't call with a darn good excuse, like they were stuck in a bad traffic jam - and I verified there was one.There won't be many bad tenants who make it through your criteria, if it's tough.