Counting multi-runs in cribbage
Not to be trite, but the score is the score! 

Announcing point contributions from the various categories (runs, pairs, same suit, correct Jack, etc.) should suffice. Note: this is what you have called "shorthand".

Of course, this all depends on the level of play. If I'm teaching the game to a new player, I would go as far as to count (the first example) as "one, two, three" (pause), "four, five, six... and a pair of Aces is eight".

In a tournament, players should know that pairs/trips/quads are worth 2/6/12, runs are calculated as (length of run) times (multiplicities of each rank involved), etc.