After taking into account vacancy, repairs, capex I'd be breaking even until my PMI drops at 20% equity.

We turned our first home into a rental and the property has around 200k in equity and the return is 9%. 

If so it might be worth trying to find an equity partner who would be OK with a preferred equity return on their down payment. 

You can buy fixer uppers and have real equity once repairs are complete.

I've got a property with some equity (rental).

Rehabbed this property and I believe it has about $90K of equity as well.

Liz - is the property  an investment property or is it a primary residence Do you need any funds  from this  equity now ….if not  - I wopuld recommend the HELOC  ...if property is an investment  property and if you want to ge the heloc in the LLCs name - you will likely find that there are not many lenders that  will be willing / able to  help with this  request

One thing to consider if you plan to cash out refinance down the road on the equity in this property then it is a good idea to have a year lease instead of month to month .

I just don’t get why the methods listed (HUD) would allow to pull out all of the initial equity to move on to the next deal.  

I'm interesting more in the buy and hold - more for long-term growth and equity.