From the views you show, the puckers dont seem to bad and if you try putting it on the LA it may just stretch the quilt the little bit it needs to smooth this out. I would at least try putting it on the LA before attemping hand quilting. You may have to square this one up by adding another border and squaring it off. If the quilt lays flat enough, go ahead and do a nice allover pattern on it. Maybe a star pantograph No need for any heirloom quilting or SITD. It's worth the try. If it doesn't work then proceed to the hand quilting and only a little time will be lost to trying and you will learn just how much of a wonky quilt a LAM can handle. It is a pretty thing.
peace