Okay, so, having established that this is something you personally use, let me try being less combative in proclaiming it broken.
So I agree, in principle, that the idea of letting your document be public is a good one. Then it could work like public-key cryptography. Even still, my concerns would be the following:
1. You are still guarding the "secret" of how you generate those passwords. That cannot be known, or your security breaks down. Is your algorithm sufficiently resilient to reverse-engineering that it won't be obvious to an attacker who sees a password that is compromised during a breach? If so, great! Personally, I can't see myself coming up with a one-way hash in my head that would not be trivial for someone else to figure out. I don't think the average person can, either.
2. You mentioned non-uniform password complexity requirements, which means that your algorithm (or algorithms) need to be able to accommodate that. I, again, feel like that would be very difficult to juggle. You're now remembering not just one algorithm, but several, and possibly several variants within.
3. Based on what you have to track just to know what algorithm to use, it sounds like your spreadsheet already has four or five columns: the site, the username, the password rules (which I assume is the "hint" that you use to tell you to use Algorithm A/B/C or Algorithm A var. 2, etc.), and the number of times compromised. At that point, I don't feel like the convenience of a "secret-free" document that doesn't need to be kept hidden outweighs the mental effort required to maintain the sheet and keep all processing within one's brain.
4. Your algorithm may be tweaked for the "max" the site will allow, but I imagine most people's are tweaked only to the minimum. What is nice about the password manager is that since I don't have to remember it, I can make the password arbitrary long. If the site allows your passwords to be up to 50 characters, I make it 50 characters. Always. I could never do that if I were forced to memorize it (unless it were a password phrase with some vowel-to-number/special char substitutions, but crackers have shown that rainbow tables already account for those).
It may well work for you. I just don't think it's a good idea for the average person.