When I was at the Smithsonian a few years back .. they do not wash any of the vintage quilts. When they are recieved they use a vacuum with a screen on the nossle and use one that has a low setting .
That being said if it was me I would machine wash on gentle cycle at a laundry mat that has a high capacity washer . Not being sure of your washers capacity or agitation method.. sometimes just stuffing a large quilt in to a washer the quilts movement can be restricted , then the agitation can strain/stress fibers that are already strained just getting it into the machine.
Hand washing /soaking in the tub is an option , just use a plastic laundry basket to remove it from the tub. Cotton fibers are their weakest when wet.