Maybe my suggestion isn't the best.
And there are good suggestions for making the game more alt-friendly.
I like the idea of all your characters on the same server going onto the friend's list.

I'd like to make some changes to my suggestion, and also stress again that it is OPTIONAL.
The players that want to continue enjoying the MSQ on their alts will NOT be forced into any action other than simply continuing the MSQ.
If you want to enjoy the MSQ, just keep doing the quests like normal. No gimmicks, no strings attached, it's just you and the MSQ.
The players that don't want to drag through it again have an option to opt-out.
After the first handful of intro quests, just check the "Opt-Out of MSQ" checkbox in the options menu, and viola.
You wont see any MSQ icons floating over NPC heads and all the MSQs will be marked as unobtainable.
Granted, this may require rezoning or, heaven forbid (sarcasm), restarting the game.
If players want to pick up wherever they left off, just uncheck the box, and take a look at the Neverending Journal to see which ones have been completed on that character (if you don't have a clue where you left off).
TLDR Players that want to enjoy the MSQ can do the quests as normal, no action required other than clicking "Accept Quest." Others can Opt-Out without losing overall progress from their main.
I'm curious to read opinions on this... (prepares for hate)