Unless you're buying a recumbent tricycle, I would think that a 2-wheeled recumbent would have all the same balance problems as a normal upright bicycle: you still need to balance and if you lose your balance, you're still going to fall over. Sure, you might not fall as far but if it happens while you're riding rather than stopped you're still going to get scraped and banged up.
Because recumbent bikes aren't nearly as popular as "standard" bikes, so finding a used recumbent that will handle someone as tall as you are may be a real challenge if you're not located in or near a bicycling mecca. I am located in a cycling mecca and the number of recumbent bikes available on Craig's List is pretty small (~20 ads out of 2500). Discard three hand trikes, a couple of tandem recumbents, and the junk bin specials and there are only 8 bikes offered for less than $500... and some of those look a little iffy.
Perhaps an adult tricycle might be a better option? There are several people in my neighborhood who use these for hauling groceries from the store to home. Dunno much about trikes, but it looks like Walmart still sells the Schwinn Meridian. Worksman sells trikes and there must be at least one more option because the ones in my neighborhood don't appear to be made by either Schwinn or Worksman.