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I don't have a source for this beyond what you already said about the text saying Chag HaPesach, but I offer this reasoning: Shavu'ot is, as you said, about the weeks (plural). For Sukkot, while ...
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#1: Initial revision
I don't have a source for this beyond what you already said about the text saying Chag HaPesach, but I offer this reasoning: Shavu'ot is, as you said, about the weeks (plural). For Sukkot, while *you* probably have at most one (and could have zero, if you use someone else's), the festival is about the *sukkot* of all Yisrael. So why is Pesach different? Each family group brought its own offering, but the actual exodus, the redemption from Egypt, was a singular event. We don't talk about our *pesachim* because we all had the same *pesach*, the same singular redemption. We have had other redemptions, but the festival is about this one. Chag HaPesach refers to the single event, while Chag HaMatzot refers to the multiple matzot and Chag HaSukkot refers to Yisrael's many sukkot.