I've never had any luck flattening plastics from the 50's.

I have had great success with 70's plastics and very good success with 60's plastics. 50's - not very good.

The method I use is similar to Chris's but does not require a sunny summer day. I sandwich the plastic between two pieces of playfield glass with some simple clamps. I then position a simple clamp light with a 60 watt light bulb for about 45 minutes. More than this gets no additional benefit. A lamp like this:
http://m.homedepot.com/p/Designers-Edge-8-5-in-Incandescent-Clamp-Light-DISCONTINUED-E-245/100664506

This has served me well for the last few years.

Let me know if you would like any guidance on this approach.

Mike O.
Team-EM