you should never try to straighten your fabric by the salvage edges- salvages need to be removed- they are never straight- and the tighter weave will (pull) everything out of whack.
it is normal to loose 2-5" of fabric when you rip it along the grain- the fabric can easily be that far out of whack from the manufacturing process.- edges always fray/curl a bit where you rip- it is important to then press line up a ruler and cut a nice (straight grain) cut.
what you are doing is (quite interesting) i will look forward to see how this comes out- sounds like it would be a pretty cool- scrappy/skewy quilt