iPad Broken Beyond Repair. What are my options?

Yes it would/does: Coverage for up to two incidents of accidental damage from handling of your iPad, each subject to a $49 service fee plus applicable tax.

http://www.apple.com/support/products/ipad.html

This used to be included on the warranty page, ""An iPhone that is ineligible for warranty service may be eligible for Out-of-Warranty (OOW) Service. For example, an iPhone that has failed due to damage or liquid damage is ineligible for warranty service but eligible for OOW service. However, certain damage is ineligible for OOW service, including catastrophic damage, such as the device separating into multiple pieces, and inoperability caused by unauthorized modifications."

This one I copied from the iPhone page a while ago but it read the same for all devices. Apple no longer has that on the page but it may still be around (just well hidden from prying consumer eyes) and if it is it may mean that if the body is bent and the screen shattered it may even be ineligible for OOW service.

You should qualify for an out of warranty replacement.

iPad Other Repairs - Official Apple Support

Standard warranty : no, accidental damage isn't covered.

AppleCare+ : no, Apple will want to see the iPad before they will sell you AppleCare+ for it.

Homeowners'/renters' insurance policies often cover accidental damage to your tech equipment. Check with them.

Mine doesn't, not even with a personal property rider and every other major insurance carrier I checked with also does not cover tablets or smartphones. Does yours and who do you have?

No such language is on the page I linked. That's why I said "should" I see no disclaimer.

The OP may very well be denied due to the specific nature of the damage.