WebDAV doesn't allow the same kind of file locking mechanisms that a network share allows. Network-share file locking has many different types of locks which can tell other computers that this file is opened by other machines and if oplocks are available (which they are on your share) even allow some communication between the various machines with that file open.
This rich locking environment is not available with WebDAV. If I'm remembering right, WebDAV has a single LOCK flag which makes it function a lot like how MS-DOS treated locks. It is for this reason that Microsoft made Sharepoint work the way it does, rather than leverage simple WebDAV.
So no, WebDAV will not work just like a network share.
Say it with me: Excel is not a database.
You're running up against the design limitations of the software: it's only got so much ability to store transactional data, so when multiple people are writing to it, it has to store a frickton of information in order to reconcile. You have so much data in it, that the transactional copies are HUGE.
Microsoft assumes (correctly) that if you have that much data, it's stored in a database, and you're just using Excel as a front end.
If you're going to work like that, you should at least knock together a little Access database. It will save you a world of headache, because it's meant to WORK like that and Excel just isn't.
@Josh: Yes, it absolutely IS leaking. When you share a document, it has to keep track of the modifications done by every user...I'll call this "transactional data" but you can just think of it as history. Since there is never an "official" version, it keeps keeping track of changes, and the document bloats up faster than Kirstie Alley in a doughnut shop.
It's by design. Someone who is an excel guru may be able to tell you how to make it stop, but the best solution is just not to use excel for data that's being constantly maintained. It's not really what it's designed for.
I am sympathetic to your problem, but it's a better solution to explain the problem to the higher-ups and work out a new procedure, than it is to try and prolong an unfortunate hack.
@Josh: If you just want to shrink it once, temporarily, copy all the data, and paste it into a new spreadsheet. THAT will kill all the metadata, guaranteed (make sure you don't select the whole sheet, but only the part with data in it) But this is a temporary solution at best.
Best Answer
When I'm trying to troubleshoot an issue that's not generating error message or other clues to direct my attention, I often run Process Monitor and watch what the application is doing with the OS. Sometimes this reveals lots of file system calls that are denied or otherwise unsuccessful. If you have a working system and a non-working one then comparing them for any obvious differences might give you the direction you're looking for.
http://technet.microsoft.com/en-us/sysinternals/bb896645.aspx
I would also recommend trying to determine whether this difference is caused by the file contents (do other spreadsheets in this location have the same problem on this machine? Sometimes spreadsheets have references to other files also -- see http://www.exceltip.com/st/Quickly_Creating_Links_between_Workbooks_in_Excel_2007/1366.html), file format (e.g. XLSX vs. XLS vs. CSV), or the application settings (a simple way to test this might be to login as another user / guest user, presumably with default preferences set, and see if the problem still occurs).