Xrm.Page.data is undefined - can't access any form data from jScript (CRM 2011)

CRM 2011 on premise, UR12.

We have a lot of javaScript in this environment that has been working fine for a few years now. At some unspecified time, our javaScript on Opportunity completely broke in a way I've never seen before. (And this isn't my first time at the rodeo.) In other words, I don't know what changed to cause this.

For example, I have a utility function:

...
	setFieldRequired : function (field, onOff)
	{
	   if (onOff) {
		   Xrm.Page.data.entity.attributes.get(field).setRequiredLevel("required"); 
	   }
	   else
	   {
		   Xrm.Page.data.entity.attributes.get(field).setRequiredLevel("none"); 
	   }
	   return null;
	},
...

Pretty straightforward, right? Well this is now erroring saying:

SCRIPT5007: Unable to get property 'setRequiredLevel' of undefined or null reference

And I'm getting this any time  I try to access or update any information in any field on the form. It's not a typo in the field name, or a syntax problem. (I even copied/pasted the field name from the UI into the script to be 100% sure.)

The only other symptom is that in F12, when the page loads, I get a million 'action is undefined' pieces.

So I took out all my custom Web Resources from the page. onLoad, I now get:

There are no iFrames or other custom code on this page, except Ribbon actions that call jScript in the web resources I removed. All the fields it references are present on the form. Basically it's a straightforward form with some complicated show/hide rules built out in JavaScript.

... Oh, and it loads fine in Chrome.

So I'm wondering, what can cause the entire Xrm.Page.data to break?

Thanks in advance!