Sorry for necro-bumping, but there is a paper doing exactly that besides various other things to eliminate timing channels claiming also to prevent attacks based on speculative execution etc: "BLACKOUT : Data-Oblivious Computation with Blinded Capabilities" https://arxiv.org/abs/2504.14654. They basically utilize another bit of CHERI for "blinded capability" and methods to mitigate potential problems you identified.
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