Okay, as far as dimension travel fics go the cliches are still the same. Here are some details

1) Harry goes back in time, but in another dimension

2) Parents are still alive - including another version of Harry (A younger one)

3) For this one I wouldn't make James as ass. Quite frankly I'm tired of all the writers that glorify Lily and put-down James. Geez... He was a jerk in Hogwarts...can't we say that a guy can change for the better? GET. OVER. IT.

4) Voldemort is dead. However, his son isn't. Considering his age, I would make him...late 20's, early 30's in age. He's the main badguy - realizing his twisted father's plans.

5) Older!Harry was/is an unspeakable. Got caught in an accident that threw him into an unstable dimensional portal.

6) Older!Harry becomes the new Divination Professor at Hogwarts.....

This is where the story becomes a bit different from other dimension!travel fics. I was going through my old D&D books and the D&D wiki on the net the other day and found an entry on divination spells. Quite an interesting selection of spells

http://www.dandwiki.com/wiki/SRD:Divination_School

For example, Occulmency and Legilimency could be considered as Divination magic. Reading another person's thoughts and emotions. Imagine walking into a crowded room and picking up stray thoughts from the passer-bys and getting a lead for a case. I'm quite sure not everyone would be proficient in Occulmency.

Being able to track or find someone based on their residual magical 'presence'. Touch a wall or object in the room where the person stayed and get a vision of the events that occurred in that room.

Just plain tracking someone. Scrying is divination. Could also be linked to remote viewing.

Detect Magic - good, evil, neutral, chaotic, lawful, whatever. Divination.

Soul Scry - being able to get into a person's head (Someone you just met, or know) and experiencing what that person is going through at the moment.

And Lastly, True Strike or pre-cognition. The Divinator's greatest advantage. Do I have to explain that one?

Check out the wiki link I posted. Its a wealth of information for story ideas and spells.

 

Um, frankly there are too many holes in your idea at the moment. Having something more interesting happening with Divination would be refreshing, but then you'd have to plausibly explain why no one was teaching these things before Harry came along, without falling back on overdone ideas like the techniques being too advanced, too dangerous or only existing in the new dimension (in which case how does Harry know them?).

Also, if you're bothered by the cliches then why not abandon them altogether? You start by saying there are too many and then go on to use them as the starting point for your story - it doesn't make sense. And why does Harry have to go back in time? Why not forward? I've only ever seen one story where that happens, and unfortunately that's my own. How about mixing stuff up and having him arrive when the Potters are old and greying and their kid a decade older than he is? Also, don't make either of the Potters jerks - it's a lot more plausible thinking that there are going to be facets of their characters that Harry just doesn't like.

Aside from all that, this new villain is the biggest turnoff from your plot bunny for me. What's the point in discarding a totally useable and well-developed villain who never expressed any interest in siring a child, for an unknown original character that you'll have to work your arse off to not make into a Voldemort caricature?

So, it's not without some potentially interesting points, but you're going to have to make it a hell of a lot more airtight for it to work.

 

Serious time-travel stories are done with. Unless you really have a seriously cool/original idea, don't do it. Look at A Black Comedy, it's sucessful because it's funny.

Harry doesn't need to be an unspeakable on a mission, just have him drop his glasses near the veil and have a banana peel placed just right. Bam. That's all an "original" idea is, taking a cliche and twisting it. Sure, you don't have to have Harry conviently wandering around the veil without his glasses, you can probably contrive a thousand reasons why he's there, and how he falls in, have fun.

OK, so Harry (presumably) survives his trip to this new universe. Now what? Divination is a perfect profession for Harry to pursue. He'll know enough of the future to be convincing (which is good for the plot), and you'll be able to have total freedom with what he teaches (try not to be too serious, forget the stupid legillimency stuff).

Then all you need is a focus: Who is the bad guy? What's Harry fighting? If you don't want to use Voldemort, fine. You'll need a conflict though. If you want Man/Man then you'll want to use Voldemort, but Man/Self and Man/Society are pretty good for HP fanfiction. Harry can be trying to change society (Dumbledore, the ministry, and "conservative" magical familes become his enemies) or Harry could be trying to change himself (this probably won't be so good since nobody knows "this" Harry, and Harry meeting resistance only from himself is lame). Just think about it. What's a conflict that provides a simple and believable conclusion and is fun?

If you want Harry to dislike the family he never had, that's fine. Be sure to stray from turning them into the Dursleys, though. That's JKR's way out. You need to give them redeeming characteristics. Lily can be a bitch, demanding that Harry stay with them, she can also judge him (if he's killed people or whatever). James is harder to write, since he's a guy, so I would suggest not making him too "good", or he'll make Lily seem more bitchy than she is.

Younger Harry sucks because he's practically a blank slate that will just emulate Harry (or side with his parents and fight against him). Young!Harry needs to be either mature/traumatized (I don't recommend that one) or have a naturally mature personality, meaning that Harry should come in Young!Harry's 5+th year, or somewhere along the line where Harry cannot just easily side with his older parallel self.

 

I don't know about you guys but from my perspective this entire stories real point is the divination part. I also find the idea of adapting some of the really cool D&D divination spells to HP. Maybe a better idea is an A/U something like Harry's first year he starts to show signs of precognativeness and picking up stray thoughts.

The first few chapters could show places where all the stray thoughts make him a bit unstable temperamentally. Also show him as he either studies on the side to gain control or Dumbles hooks him up with a teacher who helps him gain control.

From their you can show how he works through I don't know, possibly the Triwizard tournament. From this point completely diverge and make it a original story. Don't just replay the years divert.

Another possible twist is that Luna has similar abilities. They could either have a very strong friendship or possible love relationship based on their similar experiences and problems.

 

So...how does Harry defeat Voldemort's son?

If you don't have an answer to that question, better stop writing right now, because what you're lacking is called plot.

The lack of this essential characteristic has been the bane of far too many a fic to count, from Naia's The Dragonmasters to Fayr Warning's Reign of Power (that one was finished, but the ending cut off 90% of the tension that'd been building up).

It's also the reason I haven't started my own story.

 

Why the son? Why not the father?

If you cannot answer this... don't even bother.