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My apologies @amoeba. You are right. I have edited the answer to reflect the real discrepancy, which concern the default SS used by summary() when computing P-values.
I have since found the solution to this issue and have been meaning to post it here. @amoeba comment reminded me to do so. The solution is rather straightforward and I'm rather embarrassed by not having thought of it earlier. In any case, the post above has been edited for anyone downstream facing the same problem.
