"I would like to meet the writer who wrote that book very much."
Translation:O kitabı yazan yazar ile tanışmayı çok isterim.
concerning the meaning and the instrumental case I absolutely agree to your explanation.
I think it's a question about grammatical terms. As far as I know "direct object" always means "it is accusative case" at least in English.
Anyway, I do not know whether you could tell any subject of an instrumental case "direct object" in Turkish.
All it takes to make a direct object is that it receives the action of a transitive verb, right? Direct objects can be specific or general, but only the specific would take the accusative case, so there are definitely direct objects that are not accusative.
I have been trying to think of examples of verb/direct-object pairs that behave like this in English, but I think that the language is too reliant on helping verbs and prepositions! For instance, you could say "I met Marie" - where "Marie" is clearly the (specific) direct object. But if you say "I met with Marie" (which has a different meaning) - I do not think that the direct object is "with Marie." I think probably that the verb has changed to "met with" instead, and "Marie" is still the (specific) direct object.
Obviously, both tanışmak and buluşmak are transitive verbs that require direct objects, yet both phrases would take the instrumental in Turkish:
Marie'le [Marie ile] tanıştım = I met Marie.
Marie'le [Marie ile] buluştum = I met with Marie.
That is what leaves me thinking that "Marie'le" is the (specific) direct object in both, despite not having the accusative case.
I think the range of meanings for -dik- is just accusative relatives (aldığım bir tavuk 'a chicken I bought'), time relatives (tavuğu aldığımda kedim mutlu oldu 'when I bought the chicken my cat got happy'), and reported facts (çiftçi kedim tavuğumu yediğini bana dedi 'the farmer told me my cat ate my chicken').