You may be able to get a machine shop to do that, I definitely wouldn't do it by hand.
That's a tough situation. Aftermarket stuff seems to get crappier and crappier.
Any chance you can return it?
I would think the clutch from the 5 speed Caldina should work? OEM.
Your flywheel is toast too. Look how heat treated it is. It won't cause the problems your having right now, but it may cause chatter/slipping down the road. Better to replace while it's out.
Yes, I'll send it to a machine shop. And will tell them to polish. But not yet. Here's why:
I still have some suspicions about flywheel replacement thing. Since the number of old CPP correlated with SACHS and fits Hilux, Dyna, Hiace, etc., maybe getting the same clutch pressure plate with the old number will do the job.
For example, supersession of "3082 672 001" (stamped in old CPP) is "3082 313 941", which then is cross referenced again with:
Below on the left is the full image of above clutch pressure plate, and in the right (second picture) is the equivalent AISIN number of CPP OE Toyota which I got from EPC:

Notice the difference in the center, the finger gap? And the finger pointing in the left is more narrow, rather than the right which is a bit wider.
By the way, the old clutch cover is slightly thicker than the new clutch cover. Another dubious thing that the shaving of 1mm would be futile.