Just agree in principle before you go to the lawyer so you hit him with a handful of bullets to draw up the paperwork. 

The part you might need an attorney for is drawing up the operating agreement.

As that account grows, I take a ‘owners draw’ and transfer it to my personal accounts.

You will need the DP, closing costs and enough rehab money until the first draw. 

Have drawings and maybe permits going.

Don't use bait as this just will draw bugs.

Then that repeats for each phase until the project is done; this setup is often called taking "construction draws".The reason for this is that it protects the lender by never letting their loan amount get above a certain percent of the property value (LTV or loan-to-value).

Then, each of these LLCs would be owned by a Parent LLC, where the profits and losses of each individual LLC would pass through to the Parent LLC, and subsequently be passed to my personal income taxes. 

If a place draws higher revenues as a STR (in most cases seasonal but there are outliers) it is usually not a place that needs LTR all year long.  

If I draw up a contract that clearly delineates pay-ins, pay-outs and responsibilities for ownership for a property could this work?