Had a post up but notice most of the TM's weren't available yet.
I don't know what all TM's you have but going over the Elite 4 again it looks like if you're physical you may be in good fortunes.
-X-scissor hits 7 of the 22 pokemon for super effective (SE hereafter) damage. -Ice Punch (a move tutor move) hits 5 move (8 total) for 12 -Brick Break (TM from World Tournament) hits 3 more (7 total) for SE for 15 -Alternately you can use shards to teach Super Power but that lowers attack and defense afterwards. -Zen Headbut (yet another Move Tutor move) hits only Marshals pokemon SE but that adds 4 for a grand total of 19 pokemon of the 22. Actually I'm counting 20 hit SE but can't find figure out who's missing where from above but the point should be made.
Granted this list is either shard dependent with up to 3 tutor moves or BP grinding in the Tourney/Subway; however, this let's you cruse with just 1 Pokemon pretty much.
Many other options but I think this may be the best E4 set up but long term is another story. If you want long term options I'll leave that post for later as it is getting late here. Hope this helps/leads you in the right direction.