I use Logmein.com and email paperwork to them, take payment over the phone and have locks hidden onsite so they can buy those too!

It's not worth the risk that they leave as there's some inherent cost of vacancy, getting it rent-ready, changing the locks, etc.  

I locked that basement door and let the tenants know don’t let them in or we have no power.

What caught my ear was audits and W2.So, my approach would be to have a back up if your CPA/Enrolled Agent or Attorney says it's okay to do as you've laid out.

By secure I mean change the locks, install security,.....

When I flew back a month later to change the locks and do a few things to get rental ready-3 neighbors from 3 different homes came to my door.

In my lease agreement it states not to leave the door as to not let the cat out.Am I legally allowed to serve her a 3 day notice to quit for breaking multiple rules (right to quiet enjoyment, not locking the door, not leaving the door open to not let the cat out, not wearing shoes in the house)  within the first week?

The cleaner will be your eyes and ears and keep the place in top shape.

So, it's typical for them to put refinances that are locked in on the backburner for the most part.

If you have any companies that you suggest I am all ears!