Is something wrong with my LSD??

280z/300zx

So a little background. Back in 2009 when the Z first hit I special ordered a touring sport 6-speed. Loved the yellow color, it was my graduation present to myself for med school as some here know. After a year and half she was sadly totaled. Replaced her with a 2010 Nismo since ordering a 2010 replica in blue would have taken 3mo. I've owned RWD since I was 15 starting with an S14, then a toyota mini truck, then my 84 300zx (still own), and my 77 280z (still own). Not that I'm proud of it but I'm no stranger to both legal and illegal drag racing (I no longer do this). I also started auto-x 2 years ago. I'm not a professional driver by any means but I'm no stranger to appropriate technique. I also have experience with V8's via 2000 Trans Am, C6 Vette, and the new LS3 Camaro thanks to my girlfriend.

So here is my problem, my Nismo won't launch straight. It almost seems as if it has an open diff instead of an LSD. I've never felt like I could truly enjoy my car because the moment I try to get on it from a stop or coming out of a turn she loses grip more than I'm used to. I think the best comparison is my 09 370z obviously. In that car traction wasn't the greatest with the stock tires but the car at least stayed relatively straight if you gunned it from a stand still or dropped the clutch. Ton's of wheel hop, but straight. Lately it's been bothering me and I've been doing a lot of searching here. I've also been youtubing amateur racing videos of 370z's for observation. So today I decided to do a few test launches to try and figure out technique but couldn't nail it down

So if I do a simple launch at 1500-2000 rpm and feather the clutch out only applying 1/3 throttle the whole time the car will go sideways with the back end coming out for probably 10-20ft. I'm fighting the steering wheel trying to keep the car pointed straight. Finally the car hooks but as soon as I put my foot into it the tires spin. At about 5k rpm the tires stop spinning and I'm good. Once I hit 2nd gear though the back end wants to come out again. It's only for a split second but you can feel it's very unstable. I've done done rolling 1st and rolling 2nd gear launches where you just put the foot down. In both gears the back end will come out, even rolling.

Now I had similar problems in my 280z once I started adding too many mods and once I swapped in a LSD it went away. Again, my 09 370z never acted this way, it was still bad with traction, but it didn't pull sideways. My girlfriends 2010 Camaro is a blast. You can drop the clutch at any RPM and it just burns and goes no problems. Same with her old C6 Vette.

Sorry it's so long but I'm just trying to figure out if something is wrong or what. I haven't even taken it to the drag strip since I've bought it because I know I'll run horrible times. I only did one auto-x event and I was all over the place. Contrast my 09 370z saw several drag and auto-x events. My first thought is flushing the fluid per the DIY. I'm also considering replacing the tires prematurely or RE11's. So opinions please. Flame suit is on but I'm thinking something just doesn't seem right, but maybe it's just me.