Every “pair” of bits has the same pattern of AND and XOR, and the previous “carry bit” is passed into the same OR / (XOR + AND) combo to produce an output bit and the next “carry bit”. The “whole chain” is nearly right - otherwise your 44 bit inputs wouldn’t give a 45 bit output - it’s just a few are swapped over. (In my case, anyway - haven’t seen any others.) All my swaps were either in the “same column” of GraphViz output, or the next column.

So, yeah. Either “random swaps” with “nearby” outputs, because it’s nearly right and you don’t need to check further away; or use the fact that this is the well-known pattern for adding two numbers in a CPU’s ALU to generate the “correct” sequence, identify which ones are wrong, and output them in alphabetical order… The answer you need doesn’t even require you to pair them up.