Thanks to a comment left by Old Miwl on this post, I've just found out about a new website dedicated to re-opening rail links in west Wales so as to provide a new north-south route.
This is what they say about themselves:
Traws Link Cymru is a campaign to re-instate rail links in west Wales. We’re calling for rail links between Carmarthen and Aberystwyth and between Afon Wen on the Cambrian Coast line and Bangor to create a rail corridor along the west coast of Wales. We believe that closure of these routes was a mistake which should be put right. We need a rail link to boost the economy, protect the environment and connect the nation.
There have been a number of different groups campaining for this, and I don't know whether this is a brand new one or a re-incarnation or amalgamation of old groups, but contact them at email@example.com to find out more.
Meanwhile, I thought it might be a good idea to remind people of a video I put together some five years ago showing my suggestion for how a north-south rail link could be reinstated ... although my northern section isn't the same as the route proposed by Traws Link Cymru.
The video is just under 20 minutes long. If you click the bottom right hand button you can see it in full screen, but I've had to downgrade the quality slightly so that it still streams. Use the time slider to focus on any part of the route:
Carmarthen ... 3:40
Llanbedr Pont Steffan ... 6:30
Aberystwyth ... 9:40
Harlech ... 14:20
Blaenau Ffestiniog ... 16:00
The new sections are from Carmarthen to Aberystwyth, and from the Cambrian line near Llandecwyn to Blaenau Ffestiniog. The first is mainly along the line of the old railway, but with some improvements (the old route is shown paler) and the second was mentioned in more detail here.