Thanks for all the suggestions especially the reference to the heartwood colour as I was then able to pass this little gem past Chief Designer prior to purchase.
Spoke to British Hardwoods and the information that I got from them is as follows.
Ash...only comes in 3m lengths. 3/4" or 1 and 3/4" are the two finished sizes. The 3/4" stock comes out of 1" boards and the 1.75" from 2" board. So if I wanted 1" finish then I'd have to pay for the 2" board. So it's going to be 3/4" for the doors which kind of makes sense as after adding the ledge, the total thickness will be 1.5" which seems about right. I have had some suggestions from elsewhere to make the ledges slightly thicker and maybe, just maybe, I'll prep some from the ash I've had in stick for these.
The ash will come with some heartwood.