How does one build their portfolio to a level where you can quit or work part time without causing a significant reduction in the money coming in?

Test the math of your plans with a few years of price reductions and/or stagnant inflation and see how it works and if you'd be OK.  

If you find one that is experienced in investment property, they will be worth their weight in gold.It's difficult for someone to hold your hand through this process and answer your questions when we don't know you or the property.

I can continue saving cash and wait for a deal or a reduction in pricing.

I don't personally put as much weight on people with less than 5 years of experience in real estate investing.

More importantly, it "legalizes" the pet and the pet owners feel better about that, and usually stay longer.Put a weight limit on dogs. 

The ROI differential of putting $40K into a $100K property as opposed to putting $100K all cash into the same property will be significant, and that few hundred dollars of taxation plus the cost of a CPA to do the IRA tax return will be a small reduction in the benefits of using leverage.

Mudjacking raises concrete, but I question if the weight of the house is too much for this application. 

From the sounds of it, I’m leaning on assigning a weight restriction, and limiting the amount of dogs and breeds a tenant can have on my property.

For example if it is a three bedroom and they all have reasonably equal rooms and use of the house, you would take 2/3rds of the expenses (mortgage interest, depreciation, repairs, utilities you pay etc) as reductions to rental income on your tax return.