I know Fannie Mae and Freddie Mac have 75% limits on the cash out options for SFR's (70% for 2-4 multi-family). 

Close in LLC, or close with Fannie Mae 30YF with a sexy rate.Pick one...

Fannie Mae and Freddie Mac will do it at 85% LTV. 

I used the 125 K secured hard money loan as down payment on a conventional Fannie Mae loan to purchase the property.

These are Fannie Mae rules put in place in response to the flood of these loans for STR investors. 

Anywhere with high taxes and property values over $300k, I recommend you consider the live-in rehab (you live there, fix it up on the cheap, sell it 2 years later with free capital gains) on an REO (Fannie Mae Homepath has special owner occupant only deals for the first 21 days), OR focus on the quick rehab and sell (like buy for $100k, rehab for 40k, sell for 180k+ within 3-6 months).

Lets face it, a residential lender will still originate a nonconforming loan, e.g. jumbo loans (because they are over the Fannie Mae limits), non-QM loans, etc. 

Fannie Mae just released an update stating that, effective November 18th, they are increasing their max LTV requirements to 95% on a 2-4 unit property.

The ones I've talked to were aware of the Fannie Mae guidelines but had their own additional underwriting guidelines which exclude rehab costs even if they are on HUD line 120. 

I'm planning on paying cash, putting the rehab budget in escrow, and then using the Fannie Mae Delayed Financing provision.