These aren't exact figures, but I'm just using these for an example; you can look up MTOW and max fuel capacity for the correct numbers, but I think it'll suffice for an example.
What we know right now is that the J-15 can take-off with a full fuel load + 2/4 A2A missiles, which is what the J-15 and ex-Varyag is designed to do. Unlike American carriers, the ski-jump Varyag is intended to provide fleet air protection, instead of as a strike platform against enemy ships.
Actually, Russian military aviation historians have printed books that have said otherwise (regarding MTOW)
I believe at the beginning of this thread (or it may be the flanker thread) there is reference to the Su-33 book by Andrei Fomin. Totoro in this thread posted a translation of a section of the book done by paralay:
"Su-27K with incomplete filling of fuel tanks, depending on the amount of suspended missiles " air" , ranged from 25 to 28 tons while he was starting thrust 0.9-1.0 and could take off from the 1st or 2nd starting position on the deck of the ship ( the takeoff distance of 105 m ) . With full fuel tanks and maximum ammunition missiles " air" take-off weight increased to 32 tons, and thrust was reduced to 0.8. In this case vzleet aircraft had to be made with the third starting position ( takeoff distance of 195 m ) . Hence , the aircraft could start and the maximum load it with bombs and rockets ."
And the above we do not know is whether it is with 25 knots of headwind or not. I've posted and reposted the chinese scans which make the claim that Su-33 can take off from positions 1 and 2 at MTOW with 25 knots of headwind. If they're not in this thread they're in the flanker thread.
The only place I've consistently heard the idea that Su-33 couldn't take off from the kuznetsov class with full loads is from western sources, and even some official USN sources, who do not exactly show evidence proving that fighters cannot take off from ski jumps with full loads while a ship is underway, and seems more informed by bias and stereotype than anything.
Or, you can head to key forums and ask some of the Russian posters who are more knowledgeable about the military aviation of their own nation whether Su-33 could take off from Kuznetsov with full load. I did a few years ago, the answer is quite a resounding yes.
IMO the major advantage a CATOBAR carrier has isn't in its ability to launch fully loaded fighters (because ski jumps should also allow that with normal operational headwind), but rather it can possibly do so more reliably (engine failure during catapult launch won't be catastrophic during a cat launch but will be during ski jump take off). More importantly, a catapult can also reliably launch fixed wing AEWC, which is arguably one of the most important capabilities a carrier can offer. Current fixed wind AEWC designs simply are not aerodynamically designed to take off from ski jumps, and I don't see that changing, a CATOBAR carrier also has more places to spot aircraft due to no inclination.
The rest of your post I'm not going to address because of our differences to this fundamental point.