Too thick fabric for ties solution?

[Obiechick]

Customer brought in their own fabrics for chair cushions but the fabric they want for the welt and ties is almost ⅛" thick. I managed to make the welt work but it's probably not going to be comfortable but the ties will be like 1" rope and stick out like pippi long stocking pigtails- that is if You cannot see attachments on this board.they can be tied.
I made a mock up that might have been purposefully even worse than I could have done to show my boss the incompatibility but he said to just tri- fold it and don't worry about the raw edges along the sides and ends. This offends my sense of workmanship and style. Is there a quick work around (we have no surger) that would be functional and quick?