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Well I'm sure you are aware of the issues of separate tickets and the risks that come from that.
I know PVG reasonably well, it is fairly slick, the slowest stage are the two passport checks, but assuming you land and depart from T2 then you don't need to worry about that. There is a transit route via gate 71 in the arrival channel and you just need to show your documentation and onward flight details. This will be carefully checked. There is a desk for BA's ground handling agency in PVG, they may ask you to go there even if everything is in order.
Clearly if not HBO then you have to go out and come back in, you get a transit without visa via immigration, collect bags, then up to departures. It's still do-able within this timeframe, anything over 2.5 hours should be fine, assuming services are on time. Also double check that your first arrival and departure are properly cleared down and stamped, but I don't think they will be too concerned about that since it should be on their computer.