I'm not sure the follwoing is sufficient as an actual answer, but in fact I can't do much more than confirm what you already assumed, too:
The only way I can think is to memorize each line on that paper, wake up and recite those lines to Cobol Engineering before he forgets.
This indeed seems to be the intended approach. But I don't think you necessarily need to memorize each line, though. Those letters are likely not actual official letters anyway, but most probably rather sketches of his overall ideas and plans, seeing that we're in a dream and this whole documents in a safe concept has a rather metaphorical nature in the first place. Just learning the key points of his plans should be already be enough information for Cobol Engineering.
I'd like to add some general thoughts about the overall problem of this question (don't get me wrong, it isn't a bad question). The fact that the movie doesn't really explain how this whole extraction actually works, is to some degree intentional, I think, and goes hand in hand with its whole dream-aspect. All we can assume from this process of reading a letter in Saito's dream-safe is, that Cobb actually steals a thought from Saito. How this actually pans out in reality or how this thought is structued is beyond the purpose of this movie. We are just not supposed to care about the neurological reality of those things. All we know is that Cobb then somehow knows what Saito does.
By employing this escape into the dream-world, where everything is possible and where very abstract processes are represented by very concrete and tangible items and actions, the movie not only gets to "plausibly" show unusual things, like zero-gravity or stuff appearing out of nowhere, but it also achieves to completely remove the need to give explanations for such abstract processes like stealing a thought or learning things. The sometimes rather lame excuse answers like "it works somehow"/"that's the way it's written"/"the movie doesn't explain" are therefore the best and absolutely exact answers in the context of this movie. Inception achieved to remove any need for plausible explanations without actually being implausible, by employing this whole dream-metaphor, where the most difficult and abstract psychological processes are as easy as reading a letter or giving a windmill to a child.