If I had a store-front pulling $35K a month in gross sales, I can’t think of ANY circumstance where I would hire a separate company to handle the daily operations and staffing of my storefront.

In some circumstances on low end properties you don’t necessarily need to but not knowing your situation or what you are getting I’d agree with the others and say you really oughta get it

I was able to gradually raise the rent on my tenants to market value since I fixed some of the issues the previous landlord neglected.

But, there have been times when I worked too hard and neglected other responsibilities.

So the big question is, under what circumstances would someone want to offer a tenant a month-to-month lease agreement?

Let's say Party B is sole party on the mortgage at 80% LTV in each circumstance.

What do you think I should do given the circumstances?

Unless there are special circumstances not here disclosed, if it was me I'd start at a closer in community. 

Despite the circumstances this should  good learning experience. 

You'll want to discuss with your CPA who is familiar with all the facts and circumstances.