I've just read your solution and I am amazed by the comprehensive explanation. That's a big help for me and I am very thankful.
As you suggested, I'd be still trying to figure out the reason for the difference in the final results.
I had already posted this question also in https://engineering.stackexchange.com/questions/36539/bending-moment-when-there-are-no-constraints/. May I post your solution there? (of course with reference and the link to your blog)
thank you so much