It is the same amount of work to advance the cam as it is to replace it with a DR or Stage 3 cam. Either of those cams will give you much better performance from idle to full throttle than you will get from just advancing the stock cam.

Never tried it with the stock LS cam, but have tried a bit of advance and a bit of retard with a few other cams.  It was mostly out of a need to improve valve-to-piston clearance a bit or bleed down cranking pressure. Never did any definitive tests to determine if there was any improvement in performance.  If you try it, I suggest you not exceed 4 degrees (crankshaft rotation).  For instance, when the cam timing marks are lined up perfectly the crank is no more than 4 degrees before TDC (advanced) or 4 degrees after TDC (retarded).  

I doubt you will gain anything in terms of go-power.  Unlike the Kawasaki you referenced, the LS is a single overhead cam.  You can't change exhaust timing independent of intake timing.  When you advance the exhaust, you will also advance the intake.  Any improvement you realize on the exhaust will most likely be nullified by a loss on the intake.  Might be worth a try.  

If you run a stock piston or a Wiseco Pop-Top, there's plenty of grace because they don't come anywhere close to the valves at TDC.  But the Wiseco Flat-Top is a different story.  That sucker gets mighty close at TDC.  Easy to screw up and kiss a valve.  Any changes to valve timing with the Flat-Top require a careful look at valve-to-piston clearance.

Altering cam timing is pretty easy.  The cam chain sprocket on the crankshaft has 22 splines, so if you move the sprocket one-spline you change it's position 16.36 degrees, which moves the cam 8.18 degrees. The cam sprocket has 38 teeth, so if you move the chain one-tooth you change the cam position 9.47 degrees.  You can play around with the timing by advancing or retarding the sprocket on the crank and then repositioning the chain on the cam sprocket in the opposite direction. Not a perfect option but it allows taking out or adding a few degrees without hacking up any parts.  Takes a bit of patience and a degree wheel, but certainly doable.  The degree wheel is a must.

If you do it, take plenty pictures and do a nice post.  Let us know how it works out.  

There are some reference timing marks on the crankshaft and the crank sprocket.  This picture shows the sprocket retarded by 3-splines.

I have also seen guys advance their SOHC cam on their Chinese dirtbikes. They buy sprockets that advance the cam 5 degrees.