At this point its probably not a suspension issue at all. I have seen riders like JohnyP (on this forum), have the softest suspension, wobble his zx6r like an old lady out of turns, shred tires like no body's business, slip and slide all over and still set amazing lap times.
The reality is he knows how a bike should feel, understands the limits, and can even slide a little and know when the rear slippage is too much.
I would opt for better street / track tires, head to the track, drop your tire pressures as per advice from technicians at the track then take it easy and gradually progress throughout the day. Hard braking and accelerating will heat up the tires over 2 laps, then they should be sufficiently warm to lean right to the edge of the tires. The feeling is strange, but you'll notice once they are properly heated up you don't get that slipping feeling anymore, they feel SOLID under you!
I can take the same tires I felt solid on one day at the track, and the next day getting off a ramp on the highway not feel as solid on them, simply put they aren't hot enough for a full lean.
When you go around a track you heat up not only the centre of the tire, but the edges, so after 10 to 15 right hand turns at high speeds with hard braking into the corners, that's when it's hot enough!!!
Watch my video OP and you will see I made a silly mistake to push my tires following better guys on better tires. I learned how long it took to get my tires up to temp because I also went a lot of times to the track with a buddy. He became a rookie in the SOAR league and dramatically improved to better me. In our first track outings, he used to take as long as me to get his tires up to temp...street/track tires, and less aggressive riding, and no tire warmers took him 2 + laps, like me. On the day this video was shot, he was on Pirelli Super Corsa's, medium compound, 31C temps, + tire warmers. He was able to get his knee down by the second turn......I simply could not!!!!
I also know on Cayuga track for example, the left to right turns are about 1:3, and the left side of my rear tire doesn't feel as solid as the right until I am into the 3rd lap. After that, the next 20 laps are solid and never feel greasy.
I would say, riding on a highway straight up, then trying to throw it into an off ramp with some exagerated style will definately feel weird, party due to a new sensation as you push your max, but also because the tire is cold. You think it's hot but it really isn't hot enough for max lean!!!
Even on the track you will need to drop PSI from stock about 4 to 6 PSI. For example, I drop my front tire from 36PSI (street stock) to 28, then once hot they get back up to 31 with increased hot air pressure inside the tire.
On the track the techs will tell you to drop drop your pressures to whatever example but hot! So again 30C air temp and some putting about on the street is NOT a hot sticky tire.
Once you get on the track OP and you do a good 20laps touch your tires, feel how sticky they are and then you wont try any cowboy moves on the street again.
Enjoy my rear tire slip and the subsequent fall......start from 4:40 to see the start of my second lap. I shouldn't have pushed so hard on my second lap....and I made a few mistakes pushing so hard trying to keep up with my own ego. So I suggest you progress comfortably and get to know your machine. Worry about set up later. Maybe by the end of the day get a track tech to help you set it up and go out to feel the difference.
[video=youtube;lNQc9pD_y14]http://www.youtube.com/watch?v=lNQc9pD_y14[/video]
By the way, track set up is stiff and hard....not so good for the street, and at this point, you wont be shredding rear tires to even detect if you have a soft set up! But after some experience, as you push the limits, once it is set up to be stiffer you will appreciate a stiffer rear sock, stiffer forks (to stop from bottoming out under hard braking, etc), and I'm not sure a 250 has rebound dampening, so I'm not sure you will be able to counter the seesaw effect mid-corner, or even if you ever experience that at your skill level. Don't sweat set-up yet.
