Fair's fair so I consulted three dictionaries and two books on english usage: 'cannot' is the grammatically correct. However, 'can not' is acceptable when one wishes to stress 'not' (e.g. 'I can not deal with people who mention climbing and bungee jumping in the same sentence').
Why do I know this grammatical nonsense? My climbing partner's an English Ph.D. student, and 14 hours at a hanging belay, two days up a wall, 10 deg Farenheit without the wind, gives me plenty extra time to think once I'm done crying into the haul bags. (Please do excuse if 'cannot' came off a bit snotty, but then again my ex and I have found common ground arguing over 'email' vs. 'e-mail')
And for dreaming & knowing: I once knew everything, and there was no difference between me, my neighbour, or the guy on the street I too often ignore so I can get my double cappucino. I knew the man who built my table and knit my socks. An echo was both a reverberation of sound waves and the Greek nymph cursed by Zeus' wife for eternity only to answer the call of whoever shouted into the abyss.
But now this is become a confession of sorts.
Never mind, as the late great H.S.T. would say: "Buy the ticket, take the ride."
The point: Climbing, this huge expanse of infinite mountain, reminds me that I know nothing. Some negligable space in an infinite expanse, a grace. Only me and partner, some toys, and every bit of everything we've learned to get us to the top. I never could have 'dreamt' that I would find such a thing as climbing, but it is climbing that reminds me that it is the Dream to be followed if I'm ever to learn anything at all. I have to forget this 'grown-up' nonsense, artificial import attached to ideas and symbols that don't even exist.
Where was I? Yes, one trip...can anyone forward beta of any sort of the granite monoliths in the artic? Or is it the antartic?
A free or almost free route on the south or east faces Trango Tower (aka Nameless), like the Slovenian Route, Cowboy Direct, or Eternal Flame....assuming I could lead hard .12 cracks...which I cannot....but while we're dreaming, might as well go big.
Elcap- the Slovenian Route is totally reasonable - about like two-times Astroman, with the addition of a couple of 11+/12- pitches. It's an all-time classic that's accessable to most motivated climbers today. You should just go do it! The other routes you mention are probably much harder.