Taking action is key.

At $5K that is probably going to be a 2nd position note or a first position note on either a very low end home in the hood or way out in the middle of pudunk.

Does anyone have any suggestions or experience using an effective and tactful way to get the tenants to vacate quickly (incentive/legal action) ?

This one at least looks cash flow positive assuming nothing big goes after the rehab but still, it's a pretty thin margin here. 

That being said, the new goal is to find a SFH that can cover the mortgage while I save for more properties and ultimately provide positive cash flow when I decide to move out in the future.

It worked out fine for me and the new place is cash positive. 

You may need to change your strategy and surround yourself with more positive people, network with more real estate agents so they can bring you off market deals. 

Always position yourself one-step ahead of the tenant and anticipate their moves and counter-moves.

Removing the tree shows that you are not the negligent type and would be seen as a positive for you, not an admission of guilt. 

The formula is simple and is as follows, 75% of gross rent - PITI = net rental income.If net rental income is positive its added to your total income and improves your purchasing power.If net rental income is negative then its considered a liability similar to a credit card or a car loan that you gotta qualify for.Some banks have "overlays," or additional requirements they place on top of borrowers when you have rapid acquisitions of multiple properties but by no means is 2 properties in one year considered "rapid," by most lenders, however 3-5 would be its an underwriter and case by case bank "call," to make.