Are you working in sections, or joining the flowers across the whole width of the quilt?
If you break a queen size quilt into, say, 9 sections, and then put those sections together like a 9-patch block, you will never be dealing with a big heavy pieced, except for the last 2 seams (which are unavoidable).
If you still feel it's too heavy, and really can't deal with even a 30"x30"-ish piece, then you can take the paper out of all the inner hexies in the sections, with the exceptions of the last 2 rounds (just to keep it stabilized).