Using 4 wifi channels rather than 3
You hsould not try to overlap channels. You will destroy rates for both overlapped sides.
Instead, you should try to reduce power at the access points to limit their reach (and thus the area where they occupy airspace). Then you can add additional APs in the halls. The goal is to make sure that each AP only handles a manageable amount of devices, i.e. two-digit numbers when using good APs.
It requires some amount of testing how the reach of the APs is. Preferably, you should do this during actual realtime load as people dampen the signals and thus influence the reach of the APs.
I can't quite see how what you're proposing will work. Maybe I haven't quite understood it properly. I know that channels 1, 6 & 11 are the best channels to use because they don't overlap each other. While say channel 4 will use some of the frequency range of channels 1 & 6 etc. There is also a channel 14... don't use it. It's a narrower frequency that is limited to about 2Mbit/s or something. I did try it once and couldn't get it to perform.
I can only assume that you're having performance issues which is why you're looking at doing this right?
Well, having been down this track on a much smaller scale I implemented QoS and it made an enormous difference. I followed the hints from a guy on the net nicknamed toastman. He has large deployments in appartment buildings and hotels that he manages, and QoS has made what he has set up perform really well.
Realise this, that through QoS you can force your clients to be less chatty as their internet chat is slowed by the QoS giving other users a chance. Also, Bittorrent is a big cause of internet crawl. His QoS settings have helped here. Even though throughput for an individual is slowed, overall performance is increased for everyone and certain protocols which operate in bursts will still feel snappy.
Following his tips has really made a huge difference to my own set up, and even my home network.
Have a look at and read this: http://www.linksysinfo.org/index.php?threads/using-qos-tutorial-and-discussion.28349/
If in fact there are some interference problems, this link is very interesting. http://www.techedbackstage.net/2009/07/15/diagnosing-and-resolving-extremely-high-rf-utilisation/