Actually Markjo brings up a better point than mine. At what point on the runway does the shuttle normally touchdown at. If you have a 10,000 ft runway that only gives him 1400 feet to play with. Which is nothing when your moving at 230kts crossing the threshold. Im not saying it can't be done I'm just saying there would practically be no margin for error considering a go-around is impossible.
Let's say a rollout of 6000 feet is possible without drag chute (because it has been done). Estimates say that the drag chute lowers your rollout by one- or two-thousand feet. Now you're down under 5000' being conservative. That's 2500' at each end to play with. Plus whatever room there is on either side of the threshold and overruns. If you landed half way, you might eat up all 5000' (assuming the chute only gives you 1000' and not 2000' of extra margin). You'd still have your overrun area as a small margin.
I've never flown to Lajes (I think you mention you had RON'ed there, but I might be wrong and I'm too lazy to look it up). Does Lajes use EMAS? If the site NASA uses for landings has EMAS (again, I don't know that it is Lajes, but that might be an adequate if slightly less than ideal site), then a shuttle could land farther than midway down the runway and still manage a minimum of damage. The odds are against a shuttle landing a mile down from where it was aiming, but it would still be possible to land without major damage (also, I'll grant that the 6000 feet rollout was probably the product of ideal wind and atmospheric conditions, but there have been several 7000' rollouts without the chute as well).
My point is that one could operate the Orbiter with much less room than the 15000' that was said to be mandatory above. And that a landing strip of 10000' (or if daring, shorter) will not necessarily result in a landing fatal to the crew or airframe.
10,000ft is the bare minimum requirement for a survivable landing. The orbiter would melt its wheel brakes and/or run off the end of it and be heavily damaged.
A well placed landing would enable a safe landing well short of the overrun. And EMAS would enable safe operation even in the event of an overrun (barring the most extreme example of missing well over half the runway due to incompetence).