Yes, the major input came from RA/CE - LR/EM giving ARL + CEM on two lines (as you say, tedsgran).
Another helpful pair is OW - PV with the later letters usually appearing on the bottom rows this gave the likely bottom corner as OP over VW (and the bottom row could be completed to Z). It still took a bit of trial and error to line up ARL and CEM correctly but the line from A to W clinched the PI - WA pairing.
It was too far much work after the simple grid fill for my liking but they don't come around too often I suppose.