I am currently halfway through a gut rehab on a property which I completely own. I unfortunately self financed so my funds are tied up in this one house.  At this time in the project, is it possible to take out a loan...

Cash flow is mostly non-existent now, unless you find a great deal. 

The bottom line is, the strategy can open doors you didn’t even know existed.. it’s not just a tax hack, it’s a wealth-building strategy that rewards a little patience and a lot of foresight.If you’re floating around Chicago, Omaha, or even dipping your toe in the Phoenix or San Antonio scenes, I’d love to help you navigate this territory.

I am just worried this might be a mistake as it as a high cash flowing property and my mortgage rate is a low 3.125%.

There are plenty of investments that will make you money and have mortgage paydown.

this has caused significant delays with a cash out refi on an existing rental.

We are looking into houses on the lower end of the scale at first to get started for a "low risk" (we could pay mortgage out of pocket no problem even if property is vacant for 30 years) house that will give us the experience we need as rental home landlords - and I am looking down the road at potential investment ideas to keep this thing rolling.

That being said, life happens, and the mortgage police are not going to come looking for you if something unexpected happens and you have to move out of the house before one year.

For most of their existence Fannie and Freddie were privatized.  

The answer is yes, 2nd lien DSCR loans exist and more than one lender can do them, but you would probably have to up your credit score to be able to get up to a total of 75% ltv between 1st and second lienOtherwise, you would have to get lucky on a favorable appraisal.