While there is peace of mind by not having debt, I don't feel paying off my mortgage (homestead or investment properties) is the right answer. 

I rent Section 8, don't let a Gov't check give you peace of mind --- it might turn into a nightmare.Ronald Ragen taught me one thing -- trust, but VERIFY!

We’d like to give them enough fair notice to find a new place and make arrangements, but we also want to incentivize them to leave sooner and peacefully.

Yes, an inspection by an engineer would be your best bet to give you and your end-buyer peace of mind.

Basically they are harassing my tenants by calling the police on them nearly every day for various completely made up reasons, such as drug use, shouting, disturbing the peace, public drunkenness etc. 

Not unreasonably disturb the peace and quiet of other Tenants or neighbors.G.

My manager wants to evict residents on the grounds that we just gave them their third notice for lease violations - noise complaints, disturbing peace, trash in yard.My concern is that I have no police calls and no statements from neighbors backing up the violations.

That peace of mind in itself is worth not owning real estate, right?”

Prerequisite to successfully investing in real estate: understand and come to peace with the fact that it is possible to lose all, or virtually all, of your investment.

You should consider hiring a regular yard service to keep peace with the HOA.