I would cover the seams the same way (or at least a similar way) to the way they join pieces of drywall -- that is with tape and drywall mud. Only -- that's a long laborious process and you may be able to do it this way: Masking tape (not the blue stuff the regular kind) and Bondo.
So, what you do is Masking tape all the seams with 2-inch masking tape. Then, buy a 5-gallon jug of bondo and feather over the tape to cover it. Don't use too much of the catalyst and it should give you enough time to make it pretty smooth. Let it all dry overnight, then sand it smooth and paint it. Be sure to use a breathing mask when sanding.
This was what was suggested to me by my uncle who was a carpenter for 30+ years. I haven't quite gotten to that step yet, but it seems pretty sound. And I know that Bondo is what New Voyages uses to hide seams and imperfections.
I was going to mention the tape and bondo trick but you beat me to it. Back when I was in HS our shop class was charged with helping to build the sets for the school play. The Auto and Wood shop teachers worked out that solution for the massive "backer panel" for the exterior set so that it would be smooth for the art class to paint their panoramic cityscape for the "main street" scene. Worked really well, and as far as I know has been a common use fix since.