Pet Safe Mulch for My Backyard?

I have an 8 yr. old Labrador Retriever who started digging and eating the pine bark mulch in my backyard about 2 years ago. I am in process of re-doing the yard, I put in concrete pavers, stones for drainage, etc. in some areas. I put down plastic fencing covered with landscape paper over the pine bark mulch, as the whole yard is full of it, to prevent the dog from eating it.

I am looking at replacing it with something else. Would cedar mulch be a good option? or something else? I am at a loss as to what to put down on top of the landscape paper.

The vet says that the cedar mulch is an oily wood and could cause a problem if the dog ingested it or lays on it? Can you offer me any help at all as to what to put down? Taking up the pine bark mulch is a huge undertaking, but I will do it if need be. I'm really looking for a safe substitute for my dog.
I would so appreciate your help.
Thank you.

By Marybeth