Earlier quoted context omitted.
I don't think your case is very good. I read through that paper, which is not very much about the treaties, but I also didn't find any compelling arguments that the treaties say more than below. What I gather they say is Japan gives up rights to the SCS and territories they siezed from China are returned to China (RPC, ROC, whatever). However it doesn't say the Spratlys and the Paracels are returned to China, for exa…
It's not my case. It's summary of ROC/PRC argument, which predates others and had garnered major international support in a time when these disputes had no geopolitical relevance. Now it does, so the the ambiguities in language gets re-prosecuted, and is exactly what everyone nitpicks over. China thinks it sufficiently transfers islands over to Chinese sovereignty, Philippines doesn't, hence the dispute. There's also…
This is what I don't agree with. It seems you were referring to those treaties to show that the world accepted China's argument. But I don't see the evidence of that; at most they were just non-committal.
Of course it matters how good their argument is – if it was stronger than enough countries would be interested in maintaining stable international order to back them up.