The first three examples are similar in contruction, so I would choose only one of them and shut my eyes to the others. I would also opt to use the traditional analysis because I think it's easier to understand.†
[i.] An event came before another event came.
[ii.] An event came before another event.
[iii.] One event happened earlier than the other.
[iv.] One event happened earlier than the other happened.
There's no ellipsis (omission) in the first two sentences; it's just the word 'before' is used differently. In [i.], before is used as a subordinating conjuction introducing the subordinate clause (the emboldened part). So, you are right, this is a complex sentence.
[ii.], however, is not a complex sentence with ellipsis. The emboldened part is not a clause; it's a prepositional phrase headed by the preposition before and the noun phrase another event is its complement.
[iii.], on the other hand, is neither a subordinate clause nor a prepositional phrase; it's a comparative clause 'licensed' by the word "earlier".‡ Reduction (i.e. omission of some elements) is obligatory in comparative clauses, so the last sentence is ungrammatical, or at least unidiomatic.
† There's no subordinating conjunctions in modern grammar. The analysis is that before is a preposition in all your examples, but each takes a different kind of complement.
‡ Technically, it's licensed by the comparative suffix -er. But this is so trivial, so I ignore it.