Most dining chairs the back is stapled on next to the finished wood and then either double welt, gimp or decorative nails hide the staples. Also the out back can be inset so that the full finished back rails is exposed, first the out back is stapled, then webbing and foam which is applied then the inside is upholstered. From you description of trying to glue the fabric to cardboard then fastening with adhesive, sorry I can image you having good results with this kind of method.

Thanks very much for the reply, rmanbike.

None of the techniques you describe seem to apply to my chairs. These pictures might help:

http://www.danishmodernla.com/Erik_Buck_Danish_Teak_Dining_Chairs_0179.html

The backs are cardboard wrapped with fabric, then attached without any trim/decorative nails. I observed excess adhesive between the fabric where it was wrapped around the wood seat back, and the fabric wrapped around the cardboard.

Now I see what you've got, actually its quite simple, if you can get your inside back and outside back patterned to match the curve /shape of the top of the back you can sew together the 2 pieces along this shape. But this requires a sewing machine to sew along the top to make a semi cap-on back. The seam should be along the top outside edge of the back. The back post will hide the staples along the side and you staple both pieces along the underside of the back, staple inside back first then fold and staple the outside back over this.

Works best if your fabric has a little stretch and thickness, and you should try the pattern out on some scrap fabric first.

The results will be a much neater looking back then trying to make a separate attached back panel for this. And if you zoom in on the pictures in your link, I think you will see this is how they did these chairs also.