Received advice from an Aussie friend re this project.
John,
Looks like a fun and interesting project.
Some thinking out loud comments:
If it is going to be modular perhaps not having the legs might be an option as you have already noted.
Joining the modules with screws or some proprietary joiners could be easily and invisibly done by making access to the joiners when the drawers are removed.
The modules would need to allow you access to buttons that attach the top to allow for movement of the top.
The modules might each need to be structurally independent if there are to be doors and drawers otherwise it might be a nightmare having everything lined accurately but only connected with relatively flimsy joiners.
That heater might influence your design and choice of finish, it looks like a water type of heater of which I know nothing about.
Why does it have to be lightweight for Janet? If it is not going to be moved apart from when you install it, the lightweight consideration may not be important.
The entire frame in one piece would not be too heavy when you remove the drawers, shelves, doors, back, base and sides and would be structurally sounder than the modular proposal (do the calculations). The sides, base and top could be installed in the room and removed if necessary if you are moving the cabinet to another location.
Making the unit with one frame rather than modules gives you the option of having legs.