I took the cover off the oil filter on the DRZ, to find the O ring looking decidedly the worse for wear. I replaced that, cleaned everything and put it back together then started the engine again. It doesn't look like it's leaking anywhere, but there's a lot of oil to clean off from the various leaks and so on. I think this might be the end of the problems with the DRZ - now I just need to clean and degrease everything and put it all back together. Finally.