Magnum is an interesting heavy lift booster concept. Developing that or reviving Energyia wouldn't be all that difficult. However, that isn't but a tiny fraction of the R&D that has to take place before we can send humans to Mars.

1. We need to develop, test, and prove effective closed life support systems capable of supporting the crew without outside resources for at least a year. The system needs to be able to carry the crew outbound to Mars and allow for abort scenarios in case they don't make it. It does no good to send people to Mars if they arrive dead. There has been research on closed life support systems but none has been built, much less tested in space.

2. We need to build the Mars landing vehicle. Developing the Lunar Module was perhaps the most difficult challenge of the Apollo program. Read the history - the program was filled with enormous challenges, long delays, and significant overruns. Developing the Mars landing vehicle will be a considerably tougher job because it will have to survive an atmospheric entry and liftoff. Aerodynamic braking will help during the landing phase but you have to allow for heat shielding and parachutes. You also have to allow for aerodynamic drag on liftoff, which means some form of streamlining will probably be necessary. These things add to weight. In addition, the Mars lander will have to support the crew on the surface for months instead of 3 days like the LM, provide for lab space, provide a clean room airlock, carry any rover vehicles, and a host of other things not required by Apollo.

3. We need to develop space systems that are both reliable and easy to service when they break (and they WILL break). To date, such systems aren't available. These will include propulsion, electrical, life support, avionics, thermal, and structural systems.

4. We need to develop high efficiency propulsion systems with long storage lives. Today, the only such systems involve highly toxic and corrosive hypergolic propellants. If we want something with higher efficiency, then we have to consider long term storage of cyrogenic propellants (not currently available for space systems) or perhaps nuclear propulsion.

This list is by no means comprehensive, but it should serve to point out that there is a lot of R&D to do before a Mars mission has any chance of success. Developing and proving these systems will take time and money. This is where those incremental steps you're dismissing come to play. Those incremental missions like exploring an NEO allow a good proving run for the systems that can also be used to go to Mars. Only, proving the systems first increases the chances that the crew will actually make it to Mars and back alive.