GRJ, I don't know the genesis of the "original solution." That is, Chris asked some questions about adapting the specific 3PDT relay method shown below and I answered his questions at face-value.
Obviously the 3PDT method "works" as demonstrated in Chris' layout.
But to your point, yes, if it can be done with 2 SPDT relays per block, one would think it could be done with 1 DPDT relay per block.