There is no change in functionality in this commit.
Apart from clarifying what the timestamp means (it's the timestamp of the
*sender*), this intentionally breaks all the call sites, so I could have a sane
way to thoroughly audit wherever we're passing in timestamps, to see where
we're depending on them to affect sort order.
For the sake of a cleaner diff of meaningful changes, instead of "fixing"
everything in this commit, I've just added comments and renamed signatures.