Anyone make Desk Pads or Blotters? Backings?

[Cjrademaker]

I make tooled desk blotters, fairly simple, single piece of veg tan with a tooled border.

I am having trouble getting them to lay flat on their own, sometimes it works out, sometimes it doesn't and there is a little bump raised off the desks, presumably from slight stretching while tooling. I'm thinking I just need to start adding some sort of rigid backing. Anyone do anything like this? Thoughts on materials that would attach well and last?

I would like to just do two pieces of leather but I do not want to double the materials cost. That would make them prohibitively expensive. 

Id like to keep it as a single piece if anyone has any suggestions on how to get the leather to behave without a backing.

More detailed notes on process for the curious, 
8/9 oz herman oak
Cut to size and ensure squareness 
Wet with a wide mist spray bottle
Mark, swivel, bevel, tool border
Bevel and sand edges
Dry
Oil
Stain with Feibings Antiques
Dry 
Burnish Edges
Put between two heavy flat things for as long as turnaround times allow. 
Airbrush clearcoat
Put between two heavy flat things again if i've got time
Remove from heavy flat things and be frustrated by that slight but persistent bump along the edges.

[Sceaden]

I haven't done one of these but you could maybe try bag stiffener with a light lining leather.

https://www.tandyleather.com/en/product/bag-stiffener

[MADMAX22]

Do you tape the back when you tool them? I usually use the blue painters tape. It helps prevent the leather from stretching as you tool it. Once done let it dry on a flat surface then remove the tape.