With some fantastic help from Vince Parsons (and others), I've solved this problem.
Using a PhoneGap Plugin, you can create / expose a JavaScript call, which is then processed in Objective-c.
Here's the two lines you need (yes, only two lines!), and a subsequent explanation:
self.docInteractionController = [UIDocumentInteractionController interactionControllerWithURL:[NSURL fileURLWithPath:myDocumentPath]];
[self.docInteractionController presentOpenInMenuFromRect:CGRectMake(0,100,1,1) inView:UIApplication.sharedApplication.keyWindow animated:YES];
Explanation
Your input will be the file location.
In my case it's inside the app sandbox, so it looks something like:
/var/mobile/Applications/B16-HU83-GU1D-1D3NT1F13R/Documents/DocumentToExport.pdf
If you want to use an external URL, you can (with adjustments), but for my purposes it was internal.
So, with my file location as an input (let's call my input variable myDocumentPath), you just need to declare a document controller:
self.docInteractionController = [UIDocumentInteractionController interactionControllerWithURL:[NSURL fileURLWithPath:myDocumentPath]];
this creates a UIDocumentInteractionController using the interactionControllerWithURL method, which needs an NSURL variable.
We create that NSURL variable using the fileURLWithPath method, passing it our myDocumentPath.
The next line calls presentOpenInMenuFromRect Which takes a rectangle and a viewport:
[self.docInteractionController presentOpenInMenuFromRect:CGRectMake(0,0,1,1) inView:UIApplication.sharedApplication.keyWindow animated:YES];
the rectangle is created at position 0,0 with a width and height of 0,0 (GCRectMake(0,0,1,1))
and the viewport is taken from the PhoneGap application: UIApplication.sharedApplication.keyWindow
I'm reeling with joy and amazement that this only took two lines of code to fix. Granted, there's not a way to do it with JavaScript only, but it's still pretty elegant, and works great.
<script>window.location="document.pdf";</script>? It might open in Adobe Reader, or the browser window, or download depending on user preference. - antonyh