The 搭 in 搭訕 doesn't make sense to me. 搭 doesn't mean 'strike up' or 'reply'.
What exactly does 訕 mean? The embarrassing context?
From Zdic (汉典), 搭 has also the meaning of "to come into contact, to meet":
The last one in the above entry is exactly the example of 搭讪.
The same dictionary provides an entry for 讪 (but also MDGB does), where it's shown that 讪 alone means "to mock, to ridicule".
So 搭讪 together is somewhat an extension of the two meanings of 搭 and 讪, like to meet a mocking (meet = counter). MDGB again gives "to end an embarrassing silence by striking up a conversation", and Zdic "勉强找话说以消除尴尬".
PS: I vividly suggest you include Zdic in your preferred vocabulary sources. Even though the interface is in Chinese, you can easily copy-paste characters in the search bar and get decent results.
PS 2: I'm not sure why you think that words composed of 2+ characters must absolutely reflect preexisting meanings of the single characters. Languages can be productive.