Hi Lorem

I have found that the Network tool can be quite temperamental.
You have to use trial and error sometimes to get a surface just right.
I have been fiddling with an Audi TT car for a couple of month's (almost done) and have had the same sort of problems as you have encountered. Tried hundreds of ways to do the front wing but eventually cracked it with trial and error.

I have had a go with your chair and I think this is what you are after.

Notice the outer shell is just a mirror of the original - but still keeping the split down the middle, that is importatant for it to work - and then I used the back spline to creat the curves, just touching, to get the right shape.

Keep on trying and you will succeed I am sure.

Best of luck.
Malc.