How mushy are pics with the 2X?
Depends on the lens. With the 70-200 II, they're not mushy at all. (Click through and View All Sizes for a 1600 pixel version).
EOS 7D, EF 70-200mm f/2.8L
II IS USM + EF 2x II Extender @ 400mm, 1/160 s, f/5.6, ISO 3200
EOS 5D Mark II, EF 70-200mm f/2.8L
II IS USM + EF 2x II Extender @ 260mm, 1/250 s, f/5.6, ISO 400
The crane was in an enclosure, so I was shooting through wire.
The above are with the 2xII, but the 2xIII isn't really much different optically (AF is better). I'd get the 2xIII in your position...