First - I think you need to be clear about what the real goals are. Your stated purpose is that it's a memorial to fire fighters who died in 9/11. But, from your description of the teams and logistics, it's seems to be more a competition between teams of firefighters. You guys can do whatever the hell you want as far as I'm concerned, but it's confusing to this reader as to what you're trying to accomplish.
As far as the logistics are concerned - I can't add much to Steve's comments. There are several places to stay in Lone Pine, and I'd second the Hostel as a place to stay. The lobby has a large meeting area, and am reasonably sure there's a WIFI connection.
The best thing you can do in preparation is to hike, at least once a week, for 6 months (even longer is better) before doing Whitney. This assumes that none of your firefighters are regular hikers. Running helps build fitness, but it can't completely replace hiking. Do 2-3K' of elevation over a 10-12 mile RT hike on a weekly basis, and get in at least a couple of hikes where you do upwards of 6K' and 15-18 miles so people know what a more difficult hike entails. Once you've achieved a certain level of fitness, doing a big peak is mostly a head game anyway. And don't overtrain - the week before Whitney just stay rested.
And, as Steve points out - getting acclimated to altitude at someplace like Cottonwood would be a big help, but that adds 2-3 days to be of much help, which is a big time commitment and you may not have the luxury.
