Yes, for only limited forms; I'd tell you not to use 의 in that way.
Using -와의/-과의 will obscure what you mean and the form sounds literary. For example, 그와의 만남 does not clearly indicate the tense. I'd say 그와 한 만남 (past), 그와 하는 만남 (present), or 그와 할 만남 (future), depending on the relative tense. Notwithstanding, it could be inevitable when English (and Japanese) phrases like "a meeting with him" have to be translated without any context given. But in this case, I'd rather drop 의 out of the form because the following word is interpreted as a nominalized verb (만남 = 만나 (stem of the verb, 만나다) + -ㅁ (a nominalizing suffix)) and the verb (만나다) can be used with 와/과: 그와 만남.
As for your example, these sound better than 대철과의 대화 and 대철이와의 대화 to me because 대화 is a noun and 대화하다 is its verb: 대철과 한 대화 (대철과 하는 대화, 대철과 할 대화), and 대철과 대화함. Although 대철과 대화함 sounds literary and does not indicate the tense, it is still better than 대철과의 대화, in terms of simplicity. To nominalize a verb without the tense given, you may also consider using 하기 as in 대철과 대화하기.
Forms such as 대철과 대화 and 미국으로 여행 (meaning 미국 여행) are also used in everyday life. Such forms are grammatically incorrect, but they can be regarded as omissions for practical reasons. I make notes of what to do without 함 and 하기 because I know they must be attached to the ends.
Korean has been affected mainly by Chinese, Japanese, and English. For that reason, there is an argument that -와의/-과의 is equivalent to との because Koreans had never used the form until the 20th century. の is often translated as 의. To be an excellent speaker, author, or translator, you should avoid using 의 as much as possible. "Use it only when there are no ways to avoid it."
As a sidenote, there are arguments (all written in Korean) on the unnecessary use of 의: Link 1, Link 2, and Link 3.