> That requires orbital construction.
Do you know how many times two objects were successfully docked in space? And how many times they did that automatically?
> Also that imposes very severe constraints on size and shape of those pieces.
Objection to "very severe". You can have your standard fairing size full, with diameter about 5 meters and length of 15 meters or so. That's quite comparable to 6.6 meters diameter of Saturn-V payloads, is more than LEM without legs. What shape constraints you have in mind?
> This is not technology that we have demonstrated in a meaningful way.
We didn't demonstrate orbital docking technology?
> nearly twice the maximum payload of the Falcon Heavy.
But it was launched with one rocket altogether. Nobody prevents us from launching the booster stage separately and dock it with spacecraft on LEO. More, nobody prevents us from sending analog of Apollo spacecraft and LEM to the moon separately - with their own booster each. Those variants were considered in 1960-s and rejected purely on the basis of time to develop the technology - something which we have today well developed.
> Do you really want to trust this step to a rocket that has to be assembled and fueled in space?
Let me remind you that Gemini and Atlas-Agena stage docked and changed orbits in mid-1960-s, confirming that it at least can be done with then-current technology. Today ISS has a history of pushes by Shuttle, of refuels with Progress and ATV ships and I'm not sure what prevents using similar - though not identical - approach with translunar injections.