Bicycle Mechanics - Kickstand bolt stripped. How to remove?

Hello all.
Got a used bike with a huge double kickstand on it I want to remove.
Looks like what used to be an allen head on it. Stripped. The head is recessed into the stand clamp, so I can't grip it with a wrench on the outer edges of the bolt.
The bolt threads into the bottom plate of the stand, so there is no bolt or anything that will give purchase on the bootom of the stand.
I can see the bolt between the plates, but too small a space between the chainstays to get to it with a saw blade or anything to cut the bolt.

Any ideas?
Thanks for any help. I figure there must be some tricks out there for things like this.

Drill it out from below?

You have to be creative and the best (easiest) solution depends on what the kickstand is made of and what tools you hace at home.

Of you have a power drill and a friend who can hold the bike steady, drill out the bolt from the bottom, with a drill of a diameter greater than the rood of the bolt. A 5/16" drill would probably be just under ideal, but would weaken the boolt enough that it would snap pretty easily. (you should use cutting oil to dril that deep into a steel bolt, but that's easy enough to find)

Without power tools, you might have access to hacksaw through the bottom, or if you can pull the crank off, make two diagonal cuts across the top (whatever access allows), being careful not to cut into the chainstays, then carefully breaking the top plate.

Otherwise you can try using super glue to bond a 3/8" drive hex socket to the bolt, then turn it off. for this to work you have to clean everything with acetone (not nail polish remover) and bond the key in the partly turned and jammed position. You can recover the key later by putting the bolt in a vise and torquing it backward.

So that's just for starters, if none of the above are practical, just give it a good look and think like a safecracker. If you have any mechanical aptitude, something will come to mind.

Get an old Allen wrench the biggest that will fit in the bolt. Mix some JB Weld and glue it in the bolt. Make sure it is set up completely (24 hours), then back the bolt out. Sure, waste of an Allen wrench, but I know myself, I have bunches of old ones in my tools.

If you don't have enough room to swing the Allen wrench, then get a BOLT with a head just big enough to fit in the hole and JB weld it. Put two nuts on the bolt and lock them together, then put a wrench on them and back it out.

Just some things to try.

Thanks for all the great ideas. I actually just got it out. There was some scum in the hole, and I used an awl to scratch as much of it out as I could. Then I put a beefy allen wrench into the whole, and it seemed that deeper into the head, it still had enough hex wall to grab onto the allen wrench. Couple grunts worth, and it was out.

So not as drastic as I thought it might have been. Thanks for all the great tips. It will be handy to have this knowledge around if I run into the problem again.

For dealing with broken bolts, round heads etc.. a lot of these happen in the automotive part. (and I've got a lot of experience with these as an automotive mechanic in the past and a lot of wrenching on all sort of things since then)

Anyway here is my order for solving this thing:
0. Add penetrating oil (pb blaster/liquid wrench/etc)
1. try with normal wrench
2. try with impact wrench
2'. add heat from a heatgun (or a blowtorch) to loosen the paste that usually exists on the threads (almost all automotive screws have some loctite antiseize/grease/paste of some sort to prevent loosening, to be airtight, etc.. that thing is useful for unscrewing by heating the damn thing)
3. (if it's an INBUS bolt, (allen bolt), jam with a hammer the next TORX bit (http://images.esellerpro.com/41/I/655/0/draper-12200-tx-star-set.jpg))
4.a) drill a hole and use an extractor (http://0.tqn.com/d/homerepair/1/0/V/3/-/-/screw_extractor.jpg)
4.b) weld something (a nut, another bolt, etc) on the remaining head/broken bolt (works if the base is not weldable, like a broken bolt in an aluminium engine)
4.c) same thing but with glue - yet if a screw extractor failed, any glue is a lot weaker and i don't use glueing. it's messy requires time to set, etc..
5. Drill carefully trough the bolt not to touch the threads - then use a tap to chase the threads.
6. If you messed the threads, enlarge the threads and use helicoil (http://www.bombayharbor.com/productImage/0241454001201340700/Helicoil_Screw_Thread_Inserts_Helicoil_Wire_Thread_Inserts.jpg)
7. If helicoil not available for the required application, enlarge the hole bigger and use a larger bolt, or insert a reduction bushing.
8. reposition the hole elsewhere, re-engineer and make a different mounting, cut a large hole and path it with new material welded and tapped accordingly or if anything is not possible (like complex cast part like engine/transmission blocks) then it's a loss and have to be replaced.

End point is that you are at step 3. use it! I've encountered many stubborn inbus bolts (allen) that responded right away with a torx bit/impact wrench and some heat (or just the torx bit jammed is enough)

So the order to follow should be from 0 to the end.