I will be shipping from California, and would prefer to go simplest way possible. I have some boards that are quite large, and larger boxes, or at least oversized ones, seem more prone to incur damage, and generally are more problematic. I understand that removing parts, at least parts that aren't brackets, heat sinks. Iron core transformers, or caps the size of a horse's schlong, will result in a downgrade. But what about sectioning boards to fit the box? I mean, provided you get all the pieces, obviously.
You still get the same product, and make my life simpler. I don't know the details of the recovery process, but for your purposes, wouldn't 2 halves of a 1 pound board = 1 board?

You can do that but you need to keep pieces together for Boardsort to see that all the components are there. If they can't tell that the boards were all high peripheral because half look mid grade and half look high peripheral, they'll likely pay you mid grade.

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Here to learn more so I can recycle more
My grades are my own opinion and not an official grade from Boardsort

I have done it. No problem. Chris gave me the ok. Like mark141 said. Make sure it's all there and can be seen as pieces to the same board. I tie wrap my boards together. Add a little tape for good measure at times.
I use a small circular saw on a Dremel. That way you are not tearing it apart with parts scattering everywhere. You can zig zag around components to keep the integrity of the PCB.