Unfortunately, the home's mortgage is held in our names, and I performed a quit-claim deed to move the ownership into the name of the LLC.My question - how can I (legally) get a home equity loan to tap into my 25%+ capital?  

FROM your Ira you could give a loan to third party not connected with your family.

And I use a third-party integration to do mailings and follow ups.

Doubles in Irvington (good parts of irvington) perform very well.  

How Are You Performing Your Tenant Screening?

Thirdly, while your strategy of self funding the down payments will work, it is not sustainable. 

They have the means to private money which will fund 85%, while I have the remaining 15% - this is where I come in - kind of a third wheel.The agreement is that I contribute my private money and some time for basic rehab, in return for the experience, learning and 15% of net profits, and of course my 15% of initial capital, while they split the rest among themselves.They said  that they will write up all of our contracts, including mine for the 15% initial project capital, as well as, my 15% return on net profit. 

If your one lender bets wrong on the direction of rates or underwrites a large non-performing portfolio they could get a hair and start doing weird things.  

I always have a neutral third party or my attorney hold it.

@Brie Schmidt hosts a meetup on the north side (I think) the third Tuesday (I think) of the month.