I didn't post earlier because the English seems intentionally ambiguous, so no one translation is going to be ideal; you probably just have to pick something.
But since no other English speakers have spoken up, I might just say that so far, I'm not sure anyone has actually done better than the original poster's own suggestion of 'gierig / es wollend,' which seems right to me for the strongest or first sense of 'wanting.'
For 'desperate,' I also wondered about something like 'dringend' or '(ein- / vor-)dringlich' -- I'm not too clear about the shades of meaning among all those and joe's suggestion in #10, but something more in the direction of 'urgent / urging / driven.' Somehow 'verzweifelt' seems too close to despairing or sad, which I don't think is the intended meaning here.
Yes, there may also be an overtone of wanting in the sense of lacking -- 'fehlend,' 'mangelnd,' etc. But if you have to make a choice for translation, I would drop that one, because to me it seems secondary.