Yes. This is why I use a password hash function. The exact Hash function is in my head (and only my head), although it requires a lookup table for random bits. The lookup table is typically a poem, (when I was younger, I would use digits of pi, but I consider that insecure now), but can really be any sequence of words about 50+ that I can reproduce pretty much instantaneously. The exact hash algorithm is my secret, b…
Actually I like your idea of using a hash function. While thinking about your solution, I remembered that pwgen on linux (I believe its also available for windows) allows you to create a recoverable password using a sha1 hash of any file and a seed. e.g.: pwgen -1 -H yourfile#url.tld should allow you to create a unique password for each site, and it would be easily scriptable.
No batteries required.
I have a similar method, though less secure than his.