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Conventional wisdom is to save the 3rd LOR for if you get WLed and need to grovel to get off. I ignored this advice and submitted 3 with my applications and I don't think it impacted my cycle at all, so include the 3rd letter if you wish.

Re: the addendum absolutely do not write that. I can't see how it would come across as useful or helpful at all.

As to your LORs, in your case I would personally ask both and gauge their replies. I know there is interest in not wasting their time, but I'd personally put that aside. If you ask the busy, critical, major professor and he seems receptive and remembers you then I would go with that. If he seems indifferent then I would probably not use the letter he wrote, but he doesn't have to know that you didn't and at least you have it available should you want it. If he seems irritated or says no, the decision is made for you as you aren't getting the letter anyway. And then I would also ask the lecturer as it can't hurt to have her letter as a plan B and the cost to you of asking her and giving her a few printed materials is minimal.

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If they had time to scrutinize it might be slightly more positive to have a major professor write one, but ultimately most letters end up as a neutral factor anyway. If someone can write an actual great letter that compares you favorably to other students she has taught that will outweigh the subject she teaches by a huge margin.

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I had a pretty similar situation last year. I asked a friend of mine who was a dean of admissions at a law school at the time (http://www.spiveyconsulting.com) and he definitely helped. I know this seems kinda spammy but I knew him before he started his company and he helped me get into UChicago. If you email him your question he'll answer it on his blog.

So I have a weird situation on top of this. I have the two professors who agreed to write letters for me, but then I was just shooting the breeze with another professor, and he offered to write one as well, unsolicited. Do I go ahead and send in three?

If he offered take him up on it, there is no reason not to. Use your best judgment to figure out whether a certain combination of the three is better for certain schools and if you see them all as equal just send 2 and use the 3rd as a LOCI letter.