Great job at being a devil's advocate, Rob!
My turn. No you cannot do what you say as it would be a code violation. You have a panel that is expected to provide 100% load. It should only provide 80% of it's rated capacity.
But that is not what is really being hashed out here. This is not a parallel circuit where all the current flows are added. This is a series/parallel circuit where two sets of parallel loads are in series. It is also not a 120V circuit. It is a 240V circuit. The same current that flows through the first parallel circuit also flows through the second. No current goes through the neutral. That is a red herring. You can add the voltages across the two parallel circuits (120 + 120 = 240) but you cannot add the currents together any more than you could add the the currents in each turn of a coil.
Of course you know all this Bob.
And it's a great opportunity for the rest of us to sort out the puzzle to get things clearer in our heads.