I was going to suggest crosscut shank, but if they don’s sell short ribs then the chances of beef shank are slim. Veal shank is more common (think osso bucco) but if you can find beef shank, it’s great for braising.
I’m having a hard time believing that the butcher counter at your grocery doesn’t have them. Did you ask or just peruse the ready-packaged shelves? If they get entire sides of beef then they’re there, they just may not put them out. More likely, your large chain grocery is recieving cry-o-vac, processed “large” cuts of beef and then their under-trained, under-paid, “butchers” cut them down into smaller cuts, in which case you should run fleeing from the store as fast as possible.
Hit the specialty shop. I think you’ll be quite surprised that they don’t cost as much as you think. Anyway, you get what you pay for.
That recipe of Alton’s is amazing, btw. Spring for the good stuff.