But there's no real reason to insist that contemporary English and 18th-century English have to have identical grammar rules. In fact, Cambridge Grammar of the English Language (p. 91) argues that in contemporary English, can't and won't are independent words that are "negative inflections" of can and will, not true contractions. This argument is based largely on the observation that can't and won't can be used in places where cannot and will not are obsolete. (Negative inflections are uncommon in European languages but exist in other languages such as Japanese: arimasu = "to exist" and arimasen = "to be nonexistent").
Forms like won't are commonly regarded as 'contractions' of will + not, and so on, but there are compelling reasons for analysing them differently from cases like she'll (from she + will), they've (they + have), etc. Won't is, by every criterion, a single grammatical word, an inflectional form of will. She'll is not a single grammatical word, hence not an inflectional form. Rather, 'll (pronounced /l/) is a clitic form of will, i.e. a reduced form that is joined phonologically (and orthographically) to an independent word called its host. The host in the case of she'll is the pronoun she. The written forms she'll, they've, etc., are pronounced as single monosyllabic words phonologically but correspond to two-word sequences syntactically.
Evidence for this analysis is seen in:
[i] Won't/*Will not she be glad? [not replaceable by will not]
[ii] He says she'll read it, but she WON'T/will NOT.
Example [i] shows that won't is not always replaceable by will not (as she'll always is by she will), and in such cases a contraction analysis is not viable. In [ii] the [...] capitals indicate contrastive negation marked by stress. A clitic cannot bear stress (cliticisation is an extreme case of the phonological reduction that is available only for words that are unstressed). Note, for example, that in He says she won't read it, but she WILL, the stress prevents the reduction of she WILL to SHE'LL: if won't involved cliticisation like she'll, therefore, it would not occur with emphatic negation.
Best Answer
As you have noticed, contractions like shouldn't are not the same syntactically as their full versions.
Syntactically, shouldn't etc. behave like auxiliaries (eg should): they precede the subject when there is an inversion (eg in questions).
Should not is not one word, and does not behave like one word. The should is the auxiliary and precedes the subject when there is an inversion. The not is another part of the verb string, normally following the first auxiliary (I am not seeing him; I will not be seeing him; I should not have been seeing him), but in inversion it follows the subject.