LOL, Quite unique. Look 'Super' to me. But that's not an answer to your question.
The cork is to stop sliding of the coaster. Your problem is potential warping.
A change in atmosphere, temperature and humidity, may cause wood to warp.
'cause these coasters are going to go thru changes, (hot coffee, cold tea...etc)
Sandwich two pieces cross grain (like plywood) will in most cases stop any warp.