Turning the hitch over is perfectly acceptable. Many hitches, in fact, are labelled something like "four inch drop / two inch rise". And of course when you raise the front of the trailer, the back will drop (like a teeter-totter), although the rear will be lowered only about half as much as the front rises, due to the off-center placement of the axle. I'm not at all sure why the tongue weight would change, but if it does it is by a tiny amount.
I'm with Hiram, go for it. It is a quick and easy (and cheap!) fix.
Bill
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