>scale ion thrusters or solar sails or Moon based laser push-beams
OK, and how many ounces is that going to push?
Dude, manned missions are HEAVY. You have the people, their air systems, food, water redundant everything to keep people alive.
Slow pushers like what you listed make the travel time a LOT longer (say 10x, if you're optimistic), meaning you need that much more food, water, oxygen, etc - making the whole payload mind-bogglingly heavy... meaning then the engine then won't get the job done at all.