The Courtyard LBV is on Palm Parkway, around the corner form DTD, and is open. The one right next to DTD is the one than changed over to HI and currenly under renovation.
Can't help you on the shuttle/taxi problem, though. I would assume a shuttle would be cheaper but a cab quicker. I think I've seen rates to WDW hotels in the $50 range, so I would go w/ that.