China's biggest vulnerability would be its trade routes and sea lanes. If you look at it from a purely objective POV. I don't think it takes a rocket scientist to guess where the US and its allies would choose to focus their efforts in a prolonged conflict.
It currently does not have the same capacity to do sustained deployment of large CSG away from its continental shelf. It also has very sparse over seas bases and resupply depots. Its refueling assets for the PLAAF is also a small fraction of that of the US, and cannot have large fleet of strike platforms too much beyond the first island chain. The US is also beefing up its marine expeditionary units to do air and sea control around island groups.
Given this, places like the strait of Malacca, and too lesser extent Lombok and Sunda, would be major choke points that adversaries can use to choke off trade and especially energy. Some amount of increase in over land routes could mitigate some of the issues, but at a much higher cost, and possibly some delays. Other straits like Tsushima, Batanes, and Miyako would also be choked off to some extent, although those locations would be highly contested. The Indian Ocean is another area that would even be more difficult for China to do any commerce protection and the like.
Just looking at this dispassionate way, the current platforms and force structure of China would not allow much possibility of countering those types of moves.
If US uses the bulk of its forces (which will be needed) to be in the Indian ocean to cut civilian goods trades coming out of China, China shouldn't try to play convoy protection, because as you also noticed, it's force structure is not optimized for it.
Instead, China would exploit the lack of US power in East and southeast Asia, to directly strongarm neighbors into supporting Chinese war effort.
Let Americans stay west of Malacca and sink as many commercial ships they want, China will threaten SK, Japan, Thailand, anyone else in range, saying, obey our total sanctions on US and start supporting our war effort, or get invaded. US will then be starved of necessary imports to replenish both civilians and military, while China still has its in house industry fully functioning.
Then from there, it's just a matter of building more missiles, more ISR assets, and keep pot shotting at American vessels hiding in the high seas, like the u boat hunt in ww2, while the PLA island hops against US forces across the Pacific.
All the resources from its neighbors will give China more than enough boost to keep going. There's also some chance that US will piss off the global community so much by disrupting global trade that China won't even need to go fully Imperial Japan on Asia to make them all bend the knee. Not that China would hesitate about doing so, if it was a war about protecting China itself.