It could just be a year or two away (depending on your savings and credit profile). 

I would like to add my name, and eventually refinance the home in my name using my credit and income. 

As far as funding goes I have around 50k liquid right now and a pretty good credit score and my parents are always willing to cosign with me if necessary.

Then, it's a closer look at credit to justify the lack of an adequate cash flow.I once had an applicant, rather rough looking, that had about 20 beer cans in the back of the car.

She is a 1099 contractor, and we do not have any outstanding credit against the LLC.

For the "as repaired" value you will have to provide a list of improvements you plan to make.

Several investors have come in to purchase other homes (street has several other duplexes) on the street and have improved these properties as well.

One could credit the remaining folks for the deposit on file and return just the leaving tenant pro rata, but then you need a small check from the remaining tenants anyway to get the full deposit, and you never know how they have allocated or paid the deposit (or even if they are on good terms), and you rely on the kindness of strangers to return it to the leaving guy (so he does not ask you for it later).Either way, make sure it is crystal clear and communicated (I communicate it multiple times) to ensure a smooth transition and prevent problems; that may be key, get the fuzziness out and make sure no feathers are ruffled.

I have no saving, I have a part time job, I have no money and my credit is horrible.

If not, you can always try the more costly no credit/credit check point option, or pay a larger down payment to satisfy the bank.