I cut, filed and sanded one of the corners. It feels completely smooth on all sides, and integrated. I am not bothered about the "wood look" because it will be painted. The important thing is to get it as smooth as possible. Any tiny areas which will need filling, will be. Rather than fine crack polyfiller, I thought I might use "no more nails" which I used when building my cabinets; it fills small cracks well and smoothly, ready for painting.
Pic of the corner, reinforced with a corner piece cut from mounting board secured with hot glue. On the edges, I sealed the wood to the wood with UHU general purpose glue - strong bond with wood.

And a pic of the front of it:

It takes quite a while to get it nice and smooth; this one piece took me about and hour and a quarter to finish.
I now have the other side to complete, then I can start to work out what needs to go where on the top piece before cutting it.







