Compromise says, if you can't add lightness, be fancier. Can we make the frame out of batteries? Like, can we store power in load-bearing materials?

Or maybe have "spinners" on the rims, studded with alternating magnets, as the motor and the regenerative brake. If they're static relative to the wheel then they're just added mass. But if they ratchet forward on sudden deceleration, they convert kinetic energy. That should also be reversible into added power by mumble mumble hey look over there.

Or maybe avoid putting all the strength in four or five tubes, and spread it out over a crinkled-tinfoil shell. Engineer the shit out of aluminum so that two stamped sheet-metal parts form a rhombus that's stable for normal use, costs several dollars, and could probably be kicked in half.