Yes you are essentially using an ARV approach of sorts. 

Cash out refi has no impact on your tax liability upon sale. 

The utilities and so forth that you paid reduce your rental income but aren't part of the basis of the property. ie, they don't impact the sale price profit of the property.You probably should find a CPA that can help you sort all this out as it seems like you may need to file some amended returns to cover the period since you bought the property.

Additionally there's another factor...the bank of mom is going to be loaning (gifting, essentially, as an early portion of our inheritance because more than likely she'll be fortunate enough to leave my brothers and I money when she passes way too soon due to this horrific disease) us money for the down payment on the new house.

I'm interested in understanding the impact of these limitations for passive investors.

When you increase the rent, it does not impact their income and therefore, the tenant’s rent portion does not change.  

You're not wrong in considering the impacts of it.

Essentially a parent LLC that holds assets with no liabilities.

In the first scenario you are essentially free to do what you want with the money and no one is 'checking on you' but you're paying for it. 

Crowdfunding is essentially the same as old-school syndications but they are made available on the Internet.