Great point.

So for each 4 pawn cluster, 1 pawn takes another pawn, and the net result is +1 bit once the captor promotes. The remaining 2 pawns in the cluster each need 2 extra bits when promoted => 2 x 2 = 4 bits. So 5 bits per 4-pawn cluster, of which there are 4.

So maximum representation would be 162 + (5 * 4) = 182 bits?

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.