Will you be watching outside only when it's completely dark out? Or do you intend to watch while there's still light? If the latter, none of these will work and you'll need to look into something on the order of 4k+ lumens, probably more.
If the former, I'd recommend the W7000. You'll have to mount at 18ft when outdoors, and 19.5ft when indoors. You'll have more flexibility with the 5020, but less brightness in the best mode. It IS, however, much brighter in 3D mode and still throws a pretty good image in a slightly-less-than calibrated image, but at around 1600 lumens if my memory serves me.
The JVC will be the best image, but is poor for gaming and likely won't be bright enough for outside.
Panny is good, but possibly not bright enough, especially in best mode.
Sony is a great PJ, but won't be bright enough or have enough placement flexibility.
You may want to instead look at getting two projectors: a JVC to satisfy your black cravings for indoor viewing, and a less expensive one for outdoor viewing. The Viewsonic PRO8200 is a cheap and bright model. However, like I said, nothing in the $3500 range will be adequately bright for daytime or even evening viewing. There's simply too much light outside.