either a hoop or a frame would be benificial for this project- then you are not trying to handle all that fabric at once. hoop the area you are working on- with it smooth- but not tight (it's not like embroidery- you need the fabric to have give- then the rest of the quilt can just lay beside/on you as you work on an area-
some people really like the pvc type hoops/frames---others prefer a 12-14" wooden hoop.
or if available a floor frame would really make it more manageable. with it hooped both hands are free'd up to work your appliques