Car balance is done with spring rates not with adjusting damping levels, It impossible to have the best of both world, but you can compromise on one side for the other.
Think of it like in the old video games. You get 100pts to use. And can add them to either side. So you can have 100 DD and 0 track or 0 DD and 100 track or 50 dd and 50 track.
I have never been a fan of skunks products but many people on here like them, but keep in mind like you stated most people here are into having their car "slammed"
T1R has little to no damping range and it valved for super stiff springs 10k+ is my estimate. So if you want a track setup go with them, though i wasnt impressed with the particular set I had.
A couple of companys Spoon J's Mugen all offer Showa made non adjustable "performance" dampers for the Fit/Jazz. Im not quite sure if the valving is the same, but i would have to guess they are similar being made from the same company.
This option IMO is the best one, until Koni makes a damper for us. They are actual quality track/street tested dampers that will last, and will give you the best grip in both situations. I run the Mugen Sport suspension with custom spring setup.
Many of the "full coilovers" as they call them will wear out fast, because they are not valved for the springs or for the road conditions.
Also you mentioned you wanted to tune the balance. This is a common misconception that this is done with the fancy knobbers on "full coilovers". The adjustment knobs are meant to adjust the valving to your specific spring rate that is being run on that shock. Therefore there should only be one setting you should run on one set of springs. And then only change them if you change rates. To change the balance of a car, you change the spring rates front to rear or change roll bar settings of Dia.
To understand damping and setting up your suspension, this is a good read....
DGs Autocross Secrets aka Autocross to Win - Shocks