Okay, I've got another thing to complain about.
Now the model and transparent ring textures work all right in itself.
But, if the model is not centered enough, and if there's another model behind the rings... the transparent rings turn the other model behind them transparent, for those parts where it's covered by the transparent rings of the first model.

Mind you, this does not occur if the ringed planet is in the center of the view. But if I turn my craft so that the view doesn't have the ringed planet close enough to the center, then the parts of another model behind the ring suddenly turn transparent. The actual angle in which the transition occurs I don't know, but there's pretty sharp limit on it.
I think it's caused because for some reason, the game alternates the order in which it draws polygons, based on the attitude of the craft.

Dunno why, but couldn't it be simply changed by making the models in view render in order of proximity, if they don't already do so? Or, assign rendering priority to each craft - perhaps even use distance as one?
If transparent parts must be drawn first and parts behind them after that, wouldn't that take care of the problems regarding separate models obscuring each other with their transparent subobjects?