It sounds like you're willing to go tub/shower, or shower only, right?
Okay............Here's 3 units that will fit in your alcove:
The first is a plastic tub, the second is a Toto cast iron tub (Terry can certainly help you locate one of these) and the third, an Americh shower base, is the exact unit I replaced my cast iron tub with very recently.
Any plastic unit should be set on a bed of mortar, even on concrete, just so it's able to be leveled without using just shims. The cast iron tub can be shimmed.
The biggest deal is going to be lining up the drain, so you'll want to get the tub or base first, then lay it EXACTLY where it's going, and take really accurate measurements for where the drain is going down to 1/16" in either direction.
It was easy for me as I had access underneath, but you don't. A plywood panel that fits snug in the alcove floor would be a fine template to use. Just fit it into the base plate outline, then put the base over it, and trace the drain circle cutout.
As you've noticed, the units I linked to all have left-hand, right-hand, or center drains available, but they're never, ever exactly where the old one was, says Murphy:-)
This should get you started in the right direction. Of course there's nothing wrong with a tiled shower base, but these replacement units would give you more of a DIY option and should save quite a bit of money.
Best of luck!