Unattributed, but per Wikipedia: "In mid-2011, scheduled TGV trains operated at the highest speeds in conventional train service in the world,[citation needed] regularly reaching 320 km/h (200 mph) on the LGV Est, LGV Rhin-Rhône and the LGV Méditerranée." [0] You're right, though, that this is different than average speed.
Still, 300 mph would be a stretch goal for sure, but it doesn't seem ridiculous if you're starting from scratch today. The Shanghai system was built over a decade ago. At minimum, automated computer controls should be significantly improved.
I'm also operating with the assumption that the budget for such a project would be unlimited, since it's just a thought exercise.