Gasket you need is 5LV-15456-00
The only modifications I have done to mine are: K&N Filter, 2012 S1000RR rear shock, (raises the rear by 10mm using standard Dog bones) Wilbers Progressive front springs with 10w Oil, forks lifted through the yolks by 10mm and using Metzlers Sportec M7 RR tyres.
The reason for progressive springs as opposed to linear springs was because I do a lot of 2 up riding and touring. I have retained the standard Exhaust. My bike looks standard and has shocked a number of Sportbike owners on the twisty bits
, but then so does my 600
A properly serviced Fzs1000 in standard trim is a very good machine, but let down by soft suspension and tendency to understeer on acceleration out of very high speed bends. Raising the rear 10mm and dropping the front 10mm sorts it.
I have always been of the mind: Sort the handling first and then see if you need extra poke
If I feel the need to I will go the Ivanising route, but have yet to see a really convincing argument to fit the 4 degree advancer.
I do have a manual chain tensioner, which I must fit, but the number of failure instances on the FZS1000 or the R1 (Same Engine) is small.
The pulsing you describe sounds like worn tracks on the TPS, but if it is very worn it will show up a 3000 code on the rev counter. I had a similar issue and finally changed the TPS when it threw up the 3000 code and bike is much better since.
Balance the carbs first then check the TPS and service the EXUP valve and make sure it is set correctly.
Finally get it out of the garage and ride it