If you are eligible for a Fannie or Freddie loan, I would go to a mortgage broker.

The owner still owes the bank for the mortgage.

Have you sat with a couple of mortgage bankers? 

Has anyone successfully negotiated down a HUD 2nd mortgage?

You betcha it is.Because your financing will be so much cheaper (and higher LTV), you can actually offer the seller a little bit more for the house to secure the deal, and still net the same or more at the end of the day. 85% LTV instead of 70% should let you keep a little more liquid to do the reno, to boot.

Is it possible to acquire property this soon after taking a mortgage loan?

You'll never get a traditional mortgage under the LLC's name.

When getting a conventional mortgage for an investment property with value adds, would it be more beneficial to start with a 15 year mortgage and then refinance 6-12 months later with a 30 year?

Each lender has slightly different criteria for their refi products as they pertain to cash-out vs rate and term, title seasoning, reserves etc.I recommend talking to a local bank, a regional bank, a credit union, and a mortgage broker who has a variety of products.  

It is a SFH that rents for $1,100 a month and the mortgage is a few dollars under $900 per month.