If space is a problem maybe you can quilt it in parts. This means you will have to rip some seams out. Divide the quilt in 3 by 3 sections, quilt these then put them all together like a "Quilt as you go". Also adding batting is going to make this VERY heavy. You might just want to quilt the top and back together. Have you got the back fab yet, if not a nice flannel would work well. If all else fails you can always just tie them together