I think I have cracked what the "special" cam is!
Measuring the timing at 0.013" (as per the stock commando 1s cam) I get IO 52, IC 92, EO 80, EC 68 .
Comparing these timings with the Commando camshafts data sheets the timing matches the 4s cam retarded by 8 deg. within the error of the measurements.
I don't believe it is a coincidence so why would someone make a 4s cam, retard it by 8 degrees and use the same lift as the standard cam? For what purpose?
I think I may be able to suggest why the cam is retarded by 8 degrees. About 20 years ago now I developed a 500 Dommie for NZCMRR clubmans class racing down her in New Zealand. I did many dyno runs with cams and cam timing.
I tested various cam timings but one thing I settled on was the following.
My thoughts were that these days most cams are made for the Commando. And if you buy a Domi cam from any of the suppliers it will be a Commando cam with just the timing sprocket end modified. The timing will be Commando timing.
But a Dommie and a Commando have very different rod stroke ratios. Surprisingly the Dommies rod is actually 6 inches versus the 5 7/8 of the Commando. Plus of course the stroke is longer on the Commando.
The rod stroke rato on a Dommie is about 2.1 from memory while a Commando is around 1.7 ??? . Something like thst. It's 15 years since I did this.
So of course for a given crankposition the Dommie and Commando will have the piston located at a different percentage of the stroke.
My calculations suggested by proportionality you should retard a cam manufactured for a Commando by around 7 degrees if you wanted to match the piston location on a 500 Dommie.
I have never seen this discussed by anyone else and it's totally my own thoughts but it's interesting my noes seem to match your cam.
My Dommie was dynoed at 51 BHP rear wheel at 6100 rpm and at the time 15 years ago was the second fastest clubmans bike in NZ. So retarding the cam worked. I was using a PW3 cam but the same principle applies I think.