any solutions for too-small drain hole?

[noskilldiy]

We have an old porcelain sink, just moved into an old house. Tried to put in a garbage disposal, the drain pipe was rusted, plumber had to cut through it because the locknut was rusted into place, and we find the drain hole is 3 1/4", maybe 3 5/16", but definitely short of 3 1/2 inch. Now we can't install a garbage disposal, but beyond that, we can't even find a regular strainer basket (or the piece below the drain) that will fit. So we have a hole below our sink, instead of a connection to a drain. Must have been a while since they made non-standard sinks.

Is there anything we can do about this one? Anywhere to get a slightly smaller strainer basket assembly? Any way to widen the hole safely in a porcelain sink? Pretty desperate here.