You can use airdry clay to make a painting 3-dimensional.
I wet the wood first. I'm using cradled wood that you can use to paint on. I applied about a quarter of an inch and flattened it out with wet hands and shaped it.
When paperclay dries it can crack. That's not a problem. Simply wet the clay a little and put more in the crack.
Above is the back of the wood.
It's a little hard to tell what this will be now. More clay will be added, then it'll be painted. I've done things like this for about 12 years-it is so tight to the wood that the clay would have to be chisled off of it.