Everyone has given great advice, and I agree with those who think you should continue on with the quilt.
To lessen the problem with distortion, I recommend spray starching both the top and backing several times. Ideally you would have done this before pinning, but you can still do it now even with the pins in. Easiest method is to lay out the quilt flat on the floor on top of a larger flat sheet. Use spray starch, spraying from the outside edges towards the center to minimize overspray. Let dry. A fan speeds this process. Repeat, placing about 3 layers of spray starch on the one side. Then, turn the quilt over and repeat the process on the backside.
What the starch will do (even without ironing) is stabilize the fabrics so they are less easily stretched and distorted while you sew. This is useful for any straight line quilting, more so if the lines are on the bias as yours are, and even *more* so if you plan to crosshatch any of the lines. Crosshatching is where you are most likely to discover little puckers and tucks because you have excess fabric in front of the presser foot when you get to the line of stitching you have to cross.