The H&S reference is
probably (I'm guessing) based on Appendix B:
"Gil-galad before he died gave his ring to Elrond; Cirdan later surrendered his to Mithrandir." The Tale of Years, The Third Age
Granted I would agree that "before he died" doesn't necessarily mean when dying, but in any case, as far as my canon goes, however one interprets this, it is author published description versus posthumously published description in Unfinished Tales.
Can't think of anything else at the moment, although from the Council of Elrond we know Elrond could have been present at Gil-galad's death (near enough).
Anyway, I'm just wondering too