The "conventional" un-conventional method is to buy "subject to" the existing mortgage, flip, then satisfy the existing lien on your sale...

There may be a way to cash flow the property and take over the payments on the existing loan then the cost of the sale doesn't matter so much.

@Jean BolgerFannie Mae HomePath loans no longer exist, you are correct.

I would recommend you start by looking at who actually owns the land, what kind of easements exist, and whether their are any covenants that run with the land that address maintenance and or use of the land. 

Should I just offer to assume the mortgage and not give anything to the existing owner, or would it be better to offer them something so they are not losing all of their equity as well as ruining their credit?

The great majority of loans originated by small chattel lenders are retained throughout the life of the loan.

Check posts about seller financing and tired landlords.Throwing in a lump sum on existing loans doesn't effect cash flow immediately it shortens the time to the payoff and reduces interest expenses, that are deducted from income.

Tell the existing tenant that you are renting out your side for "the current market rate" and that you are going to continue renting to them "under market" as they have been good tenants but if you catch a bunch of flack from the new tenant because they tell them how much they are paying... they will be looking at an increase on the next lease,  or in 30 days if they are on a month to month.  

Based on 1.5 million you could theoretically at 75% LTV pull out 1,125,000 max. 1,125,000 - existing 750 = 375,000 to be accessed.Now say that appraisals come in low at 425k each instead of 500k.

I do plan to flip a house here or there if a great deal presents itself, and use the money made from that to either pay off existing mortgages (unfortunately then having to pay capital gains) or purchase a few more rentals.