Hi Norway,
I have the Ohlins TTX in my track bike.. I actually have that set to standard shock length.. best off to add the shims (or washers as I used) to boost your ride height, as you are definitely going to need it. It is a very slow steerer, and remember this bike was designed to be a race bike, so the factory has 'dumbed' it down for the road so it is not such a beast to ride..
I used 3 x 3.3mm washers.. so you end up with a total of pretty much 10mm which is the reccomended height raise for the 2011 / 2012 ZX10's.. and I am sure the 2013 will be exactly the same. Very simple job to do.. I can pull my ZX10's apart with my eyes closed now... you just HAVE to follow the correct procedure and watch out for a few things when removing the plastic panels or you WILL break the lugs off....
Dont bother moving the forks or anything, the front end is perfect and only needs adjustment for better handling.. it will be very firm, but depending on your weight it can be made to work really well. It it good for high 30's and low 40's at Phillip Island with the right adjustment.. and that is saying something for a stock front end...!!! But the rear shock - stock is woeful on the track.. ok for the road...(as long as you dont have a pillion on the back )
If you want any more info on this model let me know.. I have got 2 of them and had them since new...
Macca