Thank you for all your replies. I've taken a bit of a break from the discussion to experiment and reflect. Howtwosavealif3 seems to be right about the reading speed; my reading speed for kana at least has increased a lot by using my SRS, even while my SRS only contains individual words at the moment. My reading speed for kanji - well, I only read them quickly and easily if I know the word.
Fillanzea, I may not have explained well enough what I meant by spurious cues: a spurious cue need not be unrelated to the word to be learned, it is just something that you may not find in close proximity to the word in actual applications. If you would only remember 'tuna' when you were cued by 'ocean', you may not recognize it when it is used with other words instead, like 'sea'. True, using 'sea' as an extra cue will be better than using 'Obama', but deliberately courting context-dependence in words may not give optimal results, similar to one of my acquaintances who found that some students couldn't use graphs in biology class, since so far they only had made graphs in maths class!
That being said, I'm starting to see the value of context. Learning words (at the moment I'm doing Kanji -> hirigana/English) is hard, and I get lots of failed cards. Putting harder words in context at first may reduce failure rate, at a later stage the context may then be removed. I guess this is also how children first learn languages, or how we learn faces: seeing someone in the original context helps us remember who it is, until we know the person well enough that we don't need the context to jog our memory.
On the subject of learning; psychologists nowadays estimate that to achieve world-class fluency in a field (for example chess) one needs to remember about 100.000 concepts, which take at least 10 years of fulltime study to learn; I therefore estimate that average native language use (20.000 words for a native speaker, plus connotations and expressions) would take a bit more than two years full-time learning, which I think rather believable; so I don't think that learning a language is special except for the fact that almost all of us do it for our native tongue.
Vix86, you're right in that learning vocabulary is not the end-all of language learning; when you come at a point where you can just read or listen to native materials without too much trouble you may do better in either putting sentences in the SRS (especially if you're learning for exams or fast, flawless language use is important) or ditch the SRS and just read/listen to native materials. At the moment I test myself monthly on native materials, and a 300 word vocabulary (and even a 700 word vocabulary) does not seem enough for understanding much of the text yet. Though Core6k may indeed be a good idea; at the moment I'm collecting words as I go, but that is definititely not an optimal way of studying, as you'd generally want to start with words that are frequently used and (hopefully) simple. Perhaps Core6k can offer that. Actually, my Japanese reading is now quite 'interesting': texts that I've studied before and of which I remember (almost) all words due to having them in my SRS I can now read relatively easily, native unstudied material is just mainly gibberish with some familiar patterns in it (like 'wo', 'ha' and 'sono'); reading speed and understanding seems strongly related to vocabulary rather than other factors (like even grammar outside the basics (recognizing verbs, nouns, objects and subject))
I also agree with your point on which word to use in a certain context; at my work I see that with native Chinese speakers who traditionally get very little exposure to English; it seems much less frequent with native Dutch speakers who are traditionally inundated in English via subtitled TV. So I think that proper usage can be mostly learned by exposure and perhaps active reproduction; putting sentences in a SRS may not be strictly necessary, but it could indeed speed things up.