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I gone through this ... Even with a perfect sanding board and letting the sand paper do the work when you move forward and or backwards due to friction the tendency will be to apply more downwards force in the direction of travel, taking more off of the leading edge than the center. Knowing this you might play around with where you are holding the board while sanding.

When using sandpaper I had it on a long piece of plate glass. I got better results when I put a couple of layers of tape under the glass right in the center of the bottom of the glass.

Ultimately I learned to shoot with a plane and a shooting board. Now I can shoot the plates with no trouble.

what process are you using ? It takes me about 3 min. I think your technique or equipment may be more at fault.

can you post pics?

I think when you screwed them together you may have lost your flat.
If you have a table saw I would use that and the rip fence.

For whatever reason, I can't get a good joined top or back with sandpaper. I have a basic shooting board, and take a few swipes with a sharp old #5 Record plane setup for thin shavings, and I am usually good to go. I tried with sandpaper, and didn't work for me for whatever reason.

Glenn

Here's how I do it now. Takes a couple minutes. I use 100 grit PSA paper on a level, the two plates are lined up and held down as shown (but clamping and other methods would work). I use a 1/8" piece of hard board to keep the plates off the table and mark the edges with chalk so I can see any gaps left to sand, when the chalk is gone I'm done. Occasionally I use a block plane to take off wood if the plates are way off.

I tried the horizontal method and kept getting gaps as well, that all stopped for me when I switched to this method.

I used that same method. I do have a granite plate now. I think the level method and shooting board are very good methods.
A shooting board is easy to make and using a level may get you though this.