What solvents are appropriate for smoothing/finishing ASA?
ASA is Acrylonitrile styrene acrylate. According to Wikipedia:

ASA can be solvent-welded, using e.g. cyclohexane, 1,2-dichloroethane, methylene chloride, or 2-butanone. Such solvents can also join ASA with ABS and SAN. Solutions of ASA in these solvents can also be used as adhesives.
Staff, PDL (1997). Handbook of Plastics Joining: A Practical Guide. Elsevier Science. p. 515.

Solvent-welding means that the material is at least somewhat easily soluble in these fluids (they dissolve the material at the interface and as they evaporate, the former interface layers bond as if molded or welded), and the fact that the material can become an adhesive means that it is somewhat good soluble in these.
The least dangerous (and thus most advised from my side) of these 4 is 2-butanone, the others are listed as carcinogenic, and in the case of 1,2-dichloroethane, also toxic.
If these solvents can be used as a smoother similar to acetone with ABS would need testing, but a short exposition to their vapors should suffice to test this.
Addendum:
These four solvents also are able to solve Acrylonitrile butadiene styrene (ABS), which is a quite similar plastic in regards to its contents (butadiene instead of acrylate).

The acrylate rubber differs from the butadiene based rubber by absence of double bonds, which gives the material about ten times the weathering resistance and resistance to ultraviolet radiation of ABS, higher long-term heat resistance, and better chemical resistance. Wikipedia

Acetone might prove to be also a possible option, but results might differ from those on ABS.