Ah.... there are so many things that I'd change if I could, but to limit it to only one.....
I'd have made it so that the player could choose to opt out of the main quest entirely. The game would probably start the same way it already does (I really like the alternate start concept of starting in different cities depending on race, but I think the tutorial is too useful for new players to do away with it entirely-- maybe a choice, labelled "beginner" and "advanced?") The Emperor would die and the player would get the Amulet of Kings and instructions to take it to Jauffre. And when the player talked to Jauffre and he said that he wants you to go to Kvatch and get Martin, you could just flatly say, "No." Maybe have a few choices, ranging from an enthusiastic yes through maybe to an absolute no, but in any event, the option would be there to say "No."
And that would be that. Probably the player would take an immediate hit on reputation, though negative numbers are problematic, so maybe it would just effectively stay at zero for some set number of gains (in other words, for example, for the first 10 things that you do for which you would've gotten a fame point, you don't-- you basically have to work yourself out of a hole for being seen to be a coward). The Oblivion crisis would continue as scheduled-- you just wouldn't be a part of it. I think the best person then to become the Champion of Cyrodiil is Savlian Matius, who would close the gate in Kvatch and lift the siege, then take Martin to Weynon Priory and so on and so forth. All of this would be happening as the player's doing whatever it is that the player's doing. Oblivion gates would still be springing up, and the player might have to deal with that (and could even go into some if s/he so chose), but if s/he chose "No" when asked by Jauffre to go get Martin, that's it. S/he would be left out of everything else surrounding the main quest entirely. The player could keep up with what was going on through rumors and through issues of the Black Horse Courier, and eventually Savlian would prevail and be named Champion of Cyrodiil.
To make it work, there would have to be some number of better rewards for the Champion, and some number of penalties for the player not becoming the Champion. With the way it stands right now, all the player gets for finishing the main quest
Spoiler (other than just being done with it) is a statue, some lousy armor and some fame.
For that, and if one didn't have to do the MQ, there would be almost no reason to do it. So the rewards would have to be better, just to lead people to want to do it anyway, and there would have to be at least a few penalties for not doing it (say, maybe, if you leave closing the Oblivion gates up to Savlian, some of the better NPCs will get killed by Daedra, so anyone who wants to be evil can just not care, but anyone who wants to be good is going to feel a bit guilty about weaseling out of the MQ).
And that's about it, other than lots of other details that I'm sure could all be worked out....