The wording in the BBC quote, plus some others that have been posted here, suggests to me that it was the other way around. I think the discovery that Corrie could have been missed during processing (whether due to the processes or because the processes were missed) came first, and they decided to search the landfill.
In other quotes DS Elliot has said that the confirmation that the bin weight was wrong backs up their decision to search the landfill, as if the bin weight update came later.
ETA the bit about Red Lodge. I looked at that place and that name stood out to me so many times, but I always ruled it out due to the distance from the BM mast and not knowing about the transfer station and the other mast that you've mentioned!
They only ever said "the vicinity of Barton Mills and Mildenhall" they never mentioned it could be as far out as Red Lodge? I wonder if that was another thing they sort of approximated or if they did only find the signal on the BM mast? I would have thought those earlier appeals to people who might have seen him that night, and also for people in the BM and Mildenhall (as well as BSE) areas to check gardens and outbuildings would have been extended to Red Lodge if they did have the phone on that mast nearer Red Lodge at that time? Or you'd think they would have updated those advisories/requests to include Red Lodge if they found that signal later?