Does anyone remember those brightly colored plastic parson's tables and etageres that hit the market in the 70s? We had them in white, bright yellow and black at Rich's. The rep told us that a little bit of toothpaste on a damp undershirt would polish our surface scratches without damaging the shine of the surface.
A couple of weeks ago, I took some Flitz polish on a soft undershirt to the clouded headlight cover on my Solara and with minimal rubbing, brought it to like new clarity. Flitz has jeweler's rouge in it, a very fine abrasive.
I am not recommending either of these for your delicate plastic clock face, but if you cannot obtain a modern polish, these might be safe alternatives. Be sure and use an undershirt for the process and maybe try them in an inconspicuous area first. The softness and the minute holes in the knit soften the polishing.