Buy some security cameras now.

There's a chance he may have dug into walls looking for spy cameras or hidden babies.At least he's communicating with you.

I provide internet on site (mainly for the security cameras).

We even had one bored tenant install a ring camera to check when the washing machine was done so they could put it in the dryer or check if someone else had finished.

I’ve had two plumbers run the cameras and they said that if the ground was dry in December when I inspected, it may not have been spotted.

I will always have a plumber with me and have him run a camera down pipes for any possible deals that I'm interested in. and have plumber and foundation around same time so you dont pay twice for digging.

If that still doesn't clear your mind, then you can go with a PM, or you can wait outside while they look and film them entering & leaving the house as proof you were outside, or get cameras outside to independently film everything that's going on so you can have proof you were outside, etc. 

They used to be known as nanny dogs because they are generally very good with small children.You can also require the tenant get a renters policy with extra liability.  

Keypad locks, a camera doorbell, and a "panic button" ought to be enough to protect against some of the more horrifying things that someone suggested could happen. 

I wouldn’t act surprised unless you feel threatened, then buy a camera near your front door.