I follow your thought process here, but the question I would be asking myself is whether or not the purchase price of these D-class properties is actually the price. Meaning, are all of the systems in working order, or will they all need to be replaced within the first 1-2 years? Will the tenants who are willing to live in the property be going to take care of the systems and be responsible for keeping the property in good repair? Where I am in NY, there are many investors who are attracted to the lower-priced properties on the market in tougher neighborhoods because the cash flow looks attractive at the asking price. But once you factor in a new roof, furnace, oil tank, septic, and electrical, and whatever else is an issue, you end up at a price which could afford you the ability to buy a nicer C-class home in a better neighborhood without the headache of fixing everything.
Then assume you purchase the D-class property and do all of the work, you will probably invest more cash in the deal than you would have for the 15-20% down and had a whole lot more headache. If this is the road you want to go down, then why not figure out how to buy a gut job in a great neighborhood so that all the systems are starting at day one with a higher tenant class and more potential appreciation? Lastly, if the D-class neighborhood is not in the path of progress, then you're left with a property in an area which is less 'desirable' to a tenant who may be harder to manage.
This all aside, however, I bet if you speak to more banks, you will find one who can get you what you need. I recently helped a client buy a house that also had two mobile homes on the property, and the two mobiles shared a septic and well and were built in the 1950s. We went through 12 banks who said this was impossible to lend on for their banks before we found one that would, and the property cash flows great. We were able to negotiate a really good deal simply from the fact that nobody else was willing to call and really present the deal to over 10 banks to figure out the financing. Hopefuly that helps in some way.