I wonder if you could cut the metal cage in the right place, pull the liner out... and "rotate" the cage through the doorway onit's side?

Looking down from above:

[attachment=0:30zbkxsi]ibc.JPG[/attachment:30zbkxsi]

You could even make a cardboard (or even glue sticks together) flat model to try it with. Just toss it on the floor and try to "rotate" it through the doorway. When you get it to fit, use it as a template to cut the tote cage?