Sorry, got a bit late last night as there's still a lot of work to be done at Nuttlar. The plan is to open the mine and offer guided tours from this summer on with as little alterations for health and safety underground as possible and what needs to be done is generally well disguised as old. Diving is possible since last year.
There're still to larger slate mines in Germany: Magog and Rathscheck.
The vast chambers are in Spain. The company there is called CAFERSA and is part of Rathscheck group. Both mines import slate from Spain.
The Magog mine is 25 km from Nuttlar. They've introduced some modern machines for splitting and dressing in the last few years.
Hope this link works as good as the first one:
http://www1.wdr.de/mediathek/video/sendungen/lokalzeit/lokalzeit-suedwestfalen/videodieletzteschiefergrubevonnrw100.html The video shows the Magog mine.
There were some links between Nuttlar and Penrhyn in the 19th century. The first dressing machines were bought in Porthmadog. There're still 2 mining leases indicating a link: Penrhyn and Wales. They were applied for before 1865. Unluckily there's no more information available in German archives up to now.