As you & Kingshorsey say, it is quite clear that in this example there are two perfect passive infinitives that are coordinated: missam (esse) and latam esse. Note that in this example it is not only natural but compulsory to interpret/analyze missam as missam esse, i.e. as a perfect passive infinitive.
However, it is worth pointing out that it is not always easy to determine whether esse is elliptical. Consider the following example, which also contains a perfect passive participle (exstinctum):
cum auctorem senatus exstinctum laete atque insolenter tulit. (Cic. Phil. 9.7)
‘when he met the passing away of the senate’s adviser joyfully and insolently’
In this case it is more difficult to determine whether esse is elliptical or not. Syntactically speaking, this example is ambiguous:
(i) the construction auctorem senatus exstinctum can be an 'Accusativus cum Infinitivo' (AcI) structure with the verbal form esse elided (i.e. auctorem senatus [exstinctum ESSE]). Cf. the following example with esse being explicit: hoc ab isto praedone ereptum esse graviter tum et acerbe homines ferebant (Cic. Verr. 2.1.152);
(ii) the construction auctorem senatus exstinctum can be a dominant participle structure, whereby in this case there is no esse that has been elided (i.e. in this case the construction is not an AcI). The English translation above corresponds to this second reading, i.e. the one where exstinctum is a dominant participle.
Similarly, the topic of the elision of esse in compound infinitives can become crucial when discussing other subtle issues of Latin syntax. For example, at first sight, an example like the following one could be taken as a counterexample to the claim that a "dative of agent" cannot be found in a non-verbal context. However, ESSE must be postulated here with the gerundive paenitendum. Otherwise, (my claim is that) the "dative of agent" nobis would not be licensed.
Consilii nostri (...) nobis paenitendum putarem (Cic. Fam. 9.5.2). 'I should not have thought that we ought to repent of our policy’ (Evelyn S. Shuckburgh, 1908, Perseus site)
NB: incidentally this example is also interesting because it shows that, despite appearances, the accusative case of the Experiencer with impersonal paenitet/pudet...-type verbs (nos consilii paenitet) is not merely lexical/idiosyncratic. Otherwise, acc. nos would not be allowed to change to dat. nobis in the so-called "periphrastic passive" with gerundive.
