So I went ahead and ditched the swing away spare tire carrier. I have not noticed any degradation in handling or gas mileage, but I don't think either could get much worse than they were with 37" tires, roof rack, and the aerodynamics of a brick.
I bought the add-on tire carrier from Gobi for my Ranger rack. It was a simple install other than having to unbolt the rack from the roof so I could lift it high enough to get my arms underneath to tighten the bolts for the carrier bracket.
Here's some pics - the clearance is right at 8 feet now and fortunately the limit is 8'2" at my airport parking garage.