I've already got the chute, but don't know exactly what it is. De-milled US is all I know (and olive green). Anything with seams that long is going to take "serious labor and sewing"! That's why I was hoping to find out if it made sense to even invest my time in a shelter made out of this particular fabric.
I dont sew so take this suggestion with a grain of rock salt:
I would think the easiest way to take "the dome" out of a parachute is to stretch each seam out straight with a little tension, then fold over and fix with pins, tape or glue the extra cloth.
It might work to use a wooden straight edge to tension the fabric and use staples to hold everything in place while going through the machine.
Next you sew one stitch to define the new seam, trim the excess and then do one of those fancy folded over seams to make it strong.
Im only mentioning this because a lot of projects seem more manageable if you can avoid actually using a tape measure.