You may have more luck if you save one of the walls as a library part first, SEO as you were before, then put one on a hidden layer.
When you cross two walls with complex profiles on plan, one will have priority over the other and will automatically cut itself away. Saving one (or both) as library parts removes the priority based auto cutting.
Don't forget that the plan view will not be correct either as SEOs don't show on plan. The way around this may be to save the whole chair as a library part afterwards and add in a nice 2D view to the script.
My cheeky 5 minute proof of concept below!
I think yours may look better than mine!