All other things being equal dry mass tends to go up linearly whereas wet mass geometrically. For the same final payload the overall mission mass will be greater.
I don't understand. The Tsiolkovsky equation only deals with mass ratios, not absolute masses. I can see how some overhead mass might not scale linearly with size, e.g., electrical power, guidance and command systems, but these are now so light compared to structure and even rocket engines that I doubt they make much difference unless the launch vehicle is very small.
I'd think a bigger factor would be the I
sp of the rocket engines themselves, with larger ones traditionally having better performance. But I don't know the scaling laws for the current state of the art.
Good luck with sending crews on trajectories to the Moon that take months rather than days. The only advantage of lagrange points in crewed missions is they offer the possibility of leaving communications relays for the lunar far side.
My whole point was that not all of the mass to support a crewed mission has to be sent with the crew. If you send the support equipment and fuel in advance, it can take its sweet time getting there by an energy-efficient trajectory and be waiting when you launch the crew on a fast, higher-energy path.