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Yep, that increase the total in 3*3-4=5 bits, and you can repeat it 4 times, so the maximum is at least 162+4*5=182.

I'm trying to prove that is the worst case, but there are just too many cases. I guess I'll try to use a program o brute force it or just forget about it.

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Actually, given this, we believe that 4 pawns must have been captured to reach 182 bits. So at least 4 pieces no longer need colors. If we store the color mask at the end, I think we can make it variable length, and truncate when no further pieces need colors assigned.

So then we need maximum 182 - 4 = 178 bits

EDIT: Equivalently, we could suffix each non-empty piece in the sequence with an associated color bit

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