Using a straight edge, and holding 6 of my planes up against sunlight,
the gaps were bad.

I sanded and sanded, going as low as 60 wt sandpaper. Then 120 wet dry.
After two weeks of this, the soles still had hollow patches near the
mouth and heel & toe dips. The guys on oldtools.org informed me that
only my No. 3,4,4 1/2 and 5 plane need to be dead flat. I was getting
nowhere, and had expended $25 on sandpaper.

They don't need to be "entirely dead flat" at all. To be good enough for accurate
flat planing, just enough flat areas where it doesn't rock at all. If the plane is to
be used for chuting (or with a shooting board), the sides of the body need to be
an exact 90 perpendicular to the sole... that's the hard one... as you had done.

So I asked my neighbor, a machinist by trade, if his workplace had a
good surface grinder. He said they make MRI equipment for hospitals. I
gave him about 50lbs of planes and he returned two days later with
transformed tools.

The soles were within .0005" flat, with no hollows anywhere. And, the
soles are at 90 square with the sides. I gave him $50 for his trouble
and consider myself lucky. These are all Pre-WWII planes. Some are pre
WW-1 planes.

You got the great deal! ... hhhmmmm ... I know a couple of machinists!

I've heard of guys using a belt sander clamped in a vise to accomplish
the same thing. By hand, you might be digging the proverbial tunnel to
China.

The method I used worked, it took too long, but no rocking.

Gary Curtis
Los Angeles