Thanks for the suggestions.  That's a fairly complete list from my research.

I'm failing to fix this, so I'll be backing off from it for a while and giving it another go later.

What I know which doesn't fix it:

• tried from three separate clients - consistent failure for IE 10 and 11, never a problem for other browsers
• page is fully loaded before clicking the button, I've made sure so it's not that
• no dueling form tags in my layout
• switched to one of the default artisteer layouts shipped with 2.4, no luck
• not a cluster/farm, just a single IIS (tested from localhost for the most part)
• no web proxy
• machine and decryption keys are set in Web.config and recognized by IIS
• viewstatemac=false doesn't work either, although I wouldn't use that anyway since although some sources say to do it, it conflicts with MS sources which say its a serious security hole, more than just csrf, and should absolutely never be done in production
• running "aspnet_regiis.exe -i" from the .net directory and rebooting not only doesn't work, but apparently the exe isn't upgraded by 4.5 since it breaks 4.5 sites
• using installer "repair" function and rebooting doesn't work
• uninstalling 4.5.1, reinstalling through windows update, installing all updates and rebooting doesn't work either (although it reverts the app pool to .net 2.0, so you have to set back to 4.0 manually)

As you can see, I've tried a few avenues.  There may be one or two more tricks I can pull out of my sleeve, but not until I've thought of them.  My next step will probably be a fresh 2.4 install by itself to determine whether something in my directory is causing the issue.

Cheers.

Despite the lingering issue with IE on the server itself, I'm going to call this one closed.

Apparently a fresh Server 2008 R2 install with .net 4.5.1 does not necessarily have the proper registrations with IIS, since I believe it was either the install repair or the uninstallation and reinstallation of 4.5.1 from the programs and features control panel which did the trick.  Either way, if you run into this issue, do your testing from a browser on a system other than the server.

So you were right the first time, Joe, it's just that MS didn't live up to their end of the bargain it looks like.  Thanks for all of your pointers.