Zompist Bboard Again

When languages clearly mark verbs for transitivity, do verbs that take another verb as a complement appear as intransitive or transitive? Examples of verb complexes in English would be "I want to speak", "I continued to speak", "I insist on continuing", "I stopped speaking".

My question is basically, are both types of transitivity attested for such verbs?

1SG want-INTR speak-INF
1SG want-TR speak-INF
'I want to speak'

I imagine the latter easily coming about from a more redundant Latin-like accusative-and-infinitive type of construction: "1SG-NOM want-TR 1SG-ACC speak-INF", after the redundant 1SG-ACC pronoun gets dropped due to being the same referent as the subject (note: Latin does not use this construction with volō 'to want', I'm just giving this as a theoretical example). The former could come about due to verbs being quite distinct entities from regular direct object noun phrases.

Also, what about complement clauses?

1SG want-INTR 3SG speak-INF
1SG want-TR 3SG speak-INF
'I want her to speak'

The former could come about, again, due to clauses being quite different entities from direct object noun phrases.

I don't know about transitivity marking in particular. Would it make sense to check whether languages with object agreement show agreement with clausal complements, or languages with ergative case-marking treat complement clauses as genuine objects?

(A little googling suggests you'll find both patterns, sometimes within the same language. I saw a couple of things about this issue in Zulu by Claire Halpert. She takes the common Bantu pattern to be that verbs will agree with objects just if the object moves out of vP, and argues that this can happen with some but not all sorts of complement clause. Here's one thing: Clausal arguments in Bantu and beyond.)