Whether to get different letter of recommendation when supervisor's letter is bad?
As I see it, the adviser's reply is in order. He openly stated what the contents would be and emphasized the option to choose another letter, if it suits you more, without any implication that that act could be taken in a negative connotation. 

Further, the contents seem to align with the story you told here, i.e. you started a PhD, but finished with a master's degree. He states you strengths and weaknesses, which is to be expected. What is more important, he intends to accentuate you growth during your studies. This is a powerful statement from his side. As I see it, his response is objective.

Additionally, given the fact that your adviser was extremely helpful during your graduation ("day and night"), which I understand him to have taken on extra effort to see you graduate, I see no evidence that he would sabotage your attempts.

My opinion is that you should use this adviser as reference, as I seriously doubt that you could get a stronger letter from someone else (unless you neglected to mention that you had other collaborations where you fared better). Although other persons may not say anything bad about you, they can probably say also nothing positive, and luke-warm letters are not good. I would always opt for a strong letter, from someone who knows you and can attest to your journey through grad school. It is nothing unusual to have a bad start, but the fact that you saw it through and earned praise towards the end is a very good thing.

Finally, you should probably menage your expectations. You shouldn't expect that you'll find anyone willing to lie for you in a letter of recommendation. From your post, your adviser is a good guy, so, again, I think you have the best chances going with him. Or, put another way, your adviser said nothing that wasn't true, so this truth might or might not hinder your way into some institution, but that state was not induced by your adviser, he simply reports what he observed.