Mutt probably can do both, but my life is too stressed these days and my
chances to get some quiet and do any concentrating too few, too brief, and
too rare for me to tackle its learning curve. At least, for the first time
in years, I have room in my disk quota for it!
Go for mutt, especially if you're already familiar with elm. Forget
the others.
It supports a ".backward" file by means of a sendmail variable in ~/.muttrc,
just like mailx:
set sendmail='/path/to/procmail -m rcfile' (completely untested :)
mutt can sort by date or date-sent, date-received, score, subject,
threads etc., and all of these in reverse order, too. It has also
nice support for mailing lists (author reply - group reply - list reply),
and hooks to change eg. the sorting method on a per-folder basis.
Regular expression searches, but I digress :)