Welcome to the site Andy :)
Many options...
Cwmorthin is excellent, yes, get in contact witn Go Below on (01690) 710108 for the gate code. You won't have to prove anythimg to get the code.
There are however a lot of other slate mines in the area, although most will involve more of a walk.
Wrysgan - top to bottom abseil should be possible still, not been for a while, but it is not gated
Conglog - small but worth a visit, nice walk up past Llyn Cwmorthin
Rhosydd - some nice industrial remains to be seen (inclines, sheaves) and some good exploring if you look hard...
Croesor - worth a look, but you won't see a lot without SRT
Fron Boeth and Pant Mawr (and Pant Mawr tunnel), lots of short levels with some chambering on the lowest floor
Rhiwbach tramway takimg in workings alomg the route (Rhiwbach itself gated)
A few to be going on with :thumbsup:
And definitely Dinorwic. Little underground save a few short levels but probabky the best combination of walk / scenery / slate history. Apparently you're not allowed off the main footpath, but, whatever ;)
Your incline sounds a lot like Maenofferen.
my orders are to sit here and watch the world go by