(In reply to re(2): a solution
Well, I guess I don't understand your approach to getting parallel creases. Inside the parentheses, you say "For greater accuracy in the four folds, I can be folded to points on the crease IB such that the new creases formed pass through each of H, G, F and E." When I actually try it, that doesn't seem to work. In order to get a crease that passes through H, you need to join a point that is an extension of IB and off the page to another point on IB. But that's not really possible.
My approach to parallel creases is to create a new crease that is the perpendicular bisector to IB, which is done by folding I to B. Call that crease JK, where J is a point on BC. Then fold J to a point on JK such that the new crease goes through H. That newly formed crease is parallel to IB. The only problem with this, when I try it, is that I cannot form the parallel crease through point E if E F G and H are on the short side of the rectangle. Which is why I need to create my first crease by folding the short side less than 1/5 of the way towards the other short side.