How would you extend the frame on an Ikea Poang?

googler

The Poang comes with two cushions, one of which is a 'headrest'. Unfortunately, for tall folks like me, it's a shoulder rest, and the choice is either to slouch into the chair, or manually hoik the headrest upward every time you sit down.

On one chair, I've installed two guitar strap buttons on the rear of the frame to hold the headrest higher, but after time, the straps distort, and it sinks lower. There's a limit to how high the strap buttons can go, because without some part of the frame above them, the retaining straps collapse

What I need is to extend the uprights of the frame so that I can place the strap buttons higher, and still have something for the straps to hold on to.

Yes, I know I can get some wood, cut it to size, and perhaps join it to the existing frame with dowels, etc., but I'm wondering if anyone else has found the need to do this, and come up with a ready-made, possibly clip-on solution or hack that doesn't involve woodworking.....