Re: Messages.sqldb=368MB+512K
This is insanely large.
The difference with this version is that, when you use "sync N days" (as opposed to "N messages") which Exchange push requires --
-- the "messages to cache" is how many messages to cache *in addition to* those "N days", since, unlike with "sync N messages", there is no way to know how many messages those "N days" have.
In other words, please review the account level "messages to cache" and make it let's say 100 -- the app will not remove the "N days" which is the "sync" setting.
It also may be that the default "14 days" might, for you, be *a lot* of messages. If so, you may want to change to "last 10 days" or "7 days".
And then, after making those two changes, you will want to "compact the database" again. The database's size should reduce and things should be faster again.