Advise on a 240,000 sqft outdoor wireless network

Make sure your private network equipment is on 802.11a/n (5Ghz band). That provides more channels and less native interference, so you'll find more reliability.

Work with directional antennas and reduce access point transmission power. The directional antennas will reduce noise from other areas. The more isolated cells you can get, the more clients you can handle.

If you can make sure that your power is such that your APs aren't stomping all over each other and that your APs don't listen to areas they can't respond to (a stronger signal from an undesired area), then the last catch will be the omnidirectional user devices... and those will just have to play nice or figure it out.

While traditional wisdom is to use fully non-overlapping channels, do remember that some overlap may be a beneficial sacrifice for being able to get more adjacent cells. The Wifi spec demands that the further you get away from the center channel, the lower the signal strength becomes. Thus, while channels 1 and 6 dont overlap at all, adding an AP using the space of 3 or 4 will do less harm than using 2 or 5 and in a high-interference environment may work to increase overall bandwidth.

Generally, there's benefit in more expensive controllers and also in controllers that run multiple radios from a single unit. When laying out your network, you'll get a big boost in positioning things if you can turn on just a few radios at a time and map their coverage, then test with everything online at once.

Since you've got a hefty budget, consider hiring a consultant who has previously worked on conference wireless deployments. This is one of those areas where most of the work needs to be done beforehand and can't be really be fixed during an event if it wasn't right the first time.

In addition to what Jeff said: Be aware of foliage. If you do a site survey in the winter, do one again in the spring/summer. If you have a lot of trees in the area, you will have increased interference when they are full of leaves! If this is a problem for you, you can counteract this by placing the APs lower to the ground below the treeline and using direction antennae. This usually means more APs but it's better than having garbage reception for 6 months out of the year.

Also, don't just plan for coverage, plan for capacity. Many high-end APs are only spec'd for a max of 100 users with a recommendation for no more than 50. Try and plan for coverage as well as capacity.

Edit: I misread your question, I thought it was about a large outdoor area that the arena was part of. You probably don't have to worry about trees, but I'll leave this here for future visitors that may have to deal with them.