If anyone is following this and wants to try modelling their own stuff, I found what might be a way. Intusoft make a tool called SpiceMod which is part of a package they call ICAP4 though it seems the demo setup doesn't have that tool, just some very good noted on it, and modelling in general: The file WkwModels.pdf from the demo install answers a lot fo the questions I had about modelling diodes, which parameters to tweak, and extraction from data sheets.
I don't know if the lack of response to me is because of a thousand experts silently screming RTFM at me, or because it's actually asomething they DON'T KNOW. Given that Intusoft explain that this is a serious challenge for experts too, I'm assuming maybe they really don't know, so they might benefit from that file as much as I will.