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Depends on how bad it's fogged up. Mirror Glaze has two products - a cleaner and a protector. I've had some luck with both, but after a couple of years I ended up replacing the entire top. For the cost of the new top, it makes the car look like new. Was worth the investment.
A good plastic polish as you mentioned will clean that window nicely. I had the problem with my '64 and would polish the window about every few month to keep it clear. I think meguires has a polisg that will work also.
The "haze" is actually damage to the plastic window from the sun's UV rays. If it has been hazy for a long period of time, you may not be able to save it. I would try working a spot in a lower corner of the window [outside surface] with rubbing compound to see if the haze clears up. If it does, you can do the whole window with that..followed by a polish... or use some specialty product for cleaning plastic/windows. Once you get it cleared up, put a good coat of car wax on the outside and inside surfaces. That will help protect it from the UV and will keep it from getting hard. Freshen up the wax on the outside of the window every month or so to keep it nice.
I have clayed the plastic window to remove the haze then clean with Plexus plastic polish. Plexus has a mild solvent to clean and leaves a "wax" to protect.
I love Plexus, have you been introduced to the joys of Plexus?
The "haze" is actually damage to the plastic window from the sun's UV rays. If it has been hazy for a long period of time, you may not be able to save it. I would try working a spot in a lower corner of the window [outside surface] with rubbing compound to see if the haze clears up. If it does, you can do the whole window with that..followed by a polish... or use some specialty product for cleaning plastic/windows. Once you get it cleared up, put a good coat of car wax on the outside and inside surfaces. That will help protect it from the UV and will keep it from getting hard. Freshen up the wax on the outside of the window every month or so to keep it nice.
The rubbing compound will work well. I forgot to mention that I had to use it in the lower corners of mine before going to the polish.
Once that window become brittle it will be hopeless. Sound like you may have a restorable window. Good Luck.
I use Plexus on my boat eisenglass (plastic rain curtains). It cleans them very well. As someone else stated, It may be too far gone due to UV and age. GOOD LUCK!