Food for thought, no endorsement either way:
An alternative to using 1x3s or 1x4s (which are never straight) is to rip 3/4" plywood into 3"-4" strips to use for framing. You can also glue/screw them together to form an "L" for legs and attach them to the corners of the framing using cleats (yellow/orange in 1st photo). That way all the weight rests on the legs and not on screws. Unfortunately, this would leave "L" shaped indents in the carpet.
Also. if you use 3/4" plywood for the decking and shrink the modules so there is 6" overhang along the front, those legs will be out of your way as you walk around.
An alternative to cross-bracing, etc., is to simply add rails 12" or so off the floor for shelves.
I forgot to consider the bridge. That area needs to be configured so the section below the bridge can be lowered (2nd photo).
