Since we're no longer sorting by timestamp we have to ensure we save the update
info message before we save any affected message, e.g. in the case of implicit
updates.
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.
