First, medium scale for an Alembic typically means 32 inches from bridge saddles to nut. Short scale is nominally 30.75 inches, though you might measure it as 31. You might want to double check your measurement
I generally use medium scale strings on my short scale Alembics. The distance from the bridge to the tailpiece on an Alembic is longer than a Fender-style all-in-one bridge. That can add an inch or so to the length your strings need to be for the instrument, though this can vary a bit from instrument to instrument. I would definitely use regular long scale strings on a 32-34 scale Alembic. Many of these will be just a little long on the under-32 scales.
I have medium scale Chromes in play right now, and D'Addario makes a nickel round and half round in the same length. I see that Rotosound 66 and 77 strings are also available in medium, but I haven't tried either for tone or to see how they actually fit.
As a side note, the extra distance between the bridge and tailpiece can also screw up the function of exposed or taper core strings. Some sets may be at full size by the time the string crosses the bridge saddle. I had that problem with a set of LaBella roundwounds a few years back. Haven't tried anything like that since.
-bob