Hi Fix it 101;
I have had fairly good luck just running a couple 1" x 4" slats the legnth of the couch.
It does yeild some very shocked faces when one would break on occassion. But no one was ever hurt as the fall is only about as far as you are sinking now.
If that wont work for you then stuffing the couch with old rags also works.
The 1x's will not make it that hard. They have quite a bit of flex to them.
As they are riding on the springs they will still have some spring also. You can "tune " them by making them longer or shorter thereby setting them onto diffrent springs.