"With wisdom, everyday something is added. With enlightenment, everyday something is removed" - Lao Tzu, Tao Te Ching.
One can still have a goal to seek something they've never had. I've studied enlightenment for years so I understand what you're getting at but I think the way you explained it was illogical. Also I agree yes enlightenment can't be directly attained. But in a weird way, as per my quote, one can still work towards cultivating enlightenment. In the same way you can't make a seed turn into a plant but you can water it etc. The Buddha had specific instructions on how to bring enlightenment about, the noble eightfold path. But yes it's not directly attaining it as that is impossible and it's not something to attain. However it is the absence of suffering and suffering as defined by the Buddha is attachment to desire.
Over the years I've let the obsessive searching for enlightenment play itself out and eventually die down. I don't seek it anymore. As it was as you said contradictory simply because it made me suffer and it was my ego trying to be "better". As a great Zen Master once said (I forgot who) "if you meet the (Image of the) Buddha, kill him. Kill him at once and return to your own Buddha nature".
Still, talking about this stuff is just ego boosting. I haven't mentioned enlightenment in ages.
But over time my neural pathways have unwired and decalcified. And I've experienced alot of pain and release of that pain from all the programming I've had for years, even lifetimes. Eventually it does dissolve and less and less attachment suffering and egoic programming is left.
So in a way there are somewhat methods. But not directly. A famous Zen phrase is "Zen is a finger pointing at the moon. Do not confuse the finger for the moon."
Love and Light