Beautiful analysis, Gustavo! I agree with everything you've said, and love how you've given different interpretations depending on the meaning of "should," which can be interpreted in those two ways in "You shouldn't/wouldn't be so tired if you went to bed earlier."
The reading according which "shouldn't" is similar to "wouldn't" seems to be forced in "You shouldn't be so tired if you had gone to bed earlier," because it is difficult to see how "if you had gone to bed earlier" could be interpreted as anything other than a counterfactual, at least in the absence of more context.
Freeguy, I just wanted to make sure that with the label "mixed conditional" you don't understand "bad conditional." Over the years on this forum, I have always had the sense that the mixed conditional is perceived as the ugly duckling, as a dirty little construct that native speakers use. It is perfectly correct in (1)!