First of all, I really do think I would attempt a 'generational' campaign, starting during the Prequel timeline. Players could run characters within the Old republic, fighting through the clone wars and the dark-times thereafter. A party in this era might look something like this:
1) A young Jedi
2) A young Senatorial (a troubleshooter/activist for the Republic)
3) A republic military officer/agent (not a clone)
4) A fringer/smuggler type (a contact/friend of either the officer or the senatorial)
5) Wildcard—either a duplicate of one of the above or some unique type like a bounty-hunter
6) Eventually a Clone trooper—one of the lesser altered ones, so he has more free-will.
I see the plotlines covering the span of the prequels, maybe picking up shortly before Attack of the Clones, with the party being assigned to diplomatic and other 'special' operations to try and head off the coming war. Once the war started, the missions would be more oriented around that. From combat in the field to political intrigues. The Clone Wars cartoons give a pretty good indication of the kinds of missions that are possible. The story would probably climax with the fall of the Republic and the execution of Order 66. This could be very interesting for the Jedi(s) and Clone trooper in particular.
Of course, all the characters would have to be aware from the start that they would somehow have to 'transition' their character from this time period (Old Republic) to the next (Rebellion Era). This could be accomplished in a couple different ways. First of all, the player could simply keep the same character—playing an older version—the Young Senatorial could be an old senatorial. The military officer could be a retired officer, etc. In order to keep my own peculiar ideas of 'game balance', any Jedi in the party would have to either be killed (could be a very dramatic thing) or suffer a drop in power for one reason or another—becoming a 'Fallen' or 'Quixotic' Jedi (as detailed in this post). Even if the player doesn't continue playing their character (going with the option below) they could continue to exist as an NPC—maybe even a villain. Perhaps the Fringer is now a Crime boss? The young Republic Officer is now an Imperial Captain? The Young Jedi is now a Sith Agent and villain? The Clone Trooper is an Imperial Guardsman?
The second transitional option is, in my opinion, the more interesting of the two—taking up the role of a child (or student/successor) of one of the previous era characters. In this case, I would allow the character to start with most of (if not all of) the previous character's experience and shift it around a little to suit the new person. Yes, this would result in some highly skilled youngsters—but then Luke and Leia were pretty mega for being so young, too. In any case, I see the party for this era looking remarkably like that of the previous era—with either young or old 'versions' filling those roles—except for the Clone Trooper, who'd have to be thought out a bit.
The adventures in this era are already laid out in the gaming products produced by West End in what I call a 'Classic' campaign. You'd pick up right around the time of the Battle of Yavin and continue on through the Return of the Jedi storyline—and maybe even beyond for a while into the Thrawn Era.
Since this /IS/ a dream campaign (i.e. could go on longer than any real game probably ever would) I could even see transitioning the campaign once more—into a far-flung New Republic Era. Since this is MY dream universe, there wouldn't be any of that Vector prime crap (though I might make use of the villains from that in some way or another). Again, transitions could follow the above examples—though trying to continue any one character DIRECTLY from the Old Republic Era into the New would require either a very long-lived race (like a Wookiee) or a droid character type. In fact, it would probably be cool to have NPC droid henchmen follow the group through these transitions in any case.
But alas, I know that such a campaign is likely to never happen in my lifetime, but a GM can dream... a GM can dream.