I know you can get a low down payment home owners loan on a duplex but you need to be sure it will cash flow with a larger loan (higher payment).

Any perspective on which end high or low is more accurate?

Also, if you buy low and have the property rented with cashflow and a good ROI why worry about selling?

That would give me low monthly payments while leaving me plenty of reserves. 

You could rent out the home you're in now and move into the new home to get that low down-payment loan, assuming you have occupied your primary for long enough.

I plan on low balling an offer.

Unless you are highly leveraged and don't have much "skin in the game" as they say, your cash on cash return will be very low.  

If you're hurting to sell maybe go ahead and take the hit but if its Low DOM then maybe put it back out there and get some conventional offers that are willing to meet in the middle or make up the difference.

Perhaps I will run into someone who can shed some light on what I should do.

A lot of lenders may tell you the appraisal is free however its not free if you dont close you will still pay for the appraisal typically (its only free and credited back at the end or at the closing table).The other part is to make sure rates are where you want them to be (low enough).