The sentence in question: 取材を進めてみると、あまり結婚式が行われないはずの“平日”を最大限活用しようという、逆転の発想が見えてきました。
My attempt at translation: When we move forward with our news, the concept of a change to "let us make maximum use of ordinary days where it is to be expected that almost no marriage ceremony will happen" comes to mind.
I have a lot of problems understanding and translating this sentence. The biggest issue I had was finding a way to implement 最大限活用しよう in a meaningful way, especially when considering the context. In the sentence before, we've heard that the wedding industry is facing adverse circumstances due to the increase of marriages without any celebration, party etc.. So I guess this sentence still refers to the wedding industry, which must make the best of the situation and do something "productive" during those days of the week on which are very unlikely to have any kind of marriage take place at all. I must admit though that I chose this interpretation mostly due to the fact that I couldn't find any other way to get to a halfway meaningful sentence^^ Therefore, I guess it is at the very least partially wrong xD
The second biggest problem I faced was という. I learned on this forum that the pattern "A という B だ" basically can be interpreted as " A is B". I apologize in advance if I'm wrong (again) ^^ With this premise, I interpreted あまり結婚式が行われないはずの“平日”を最大限活用しようという as an attribute to 逆転の発想. I went for the "lets do" interpretation of the volitional form in 最大限活用しよう because that was the only way I could muster a meaningful translation...^^
Well and my third biggest problem stems from the second one. I had a hard time coming up with a comprehensible, syntactically functional translation of the full construct あまり結婚式が行われないはずの“平日”を最大限活用しようという、逆転の発想. First I tried going with a common relative clause starting with "which": "The concept of a change which (says that), "...". This made the sentence very obstructive though so I decided against it. Instead I used the preposition "to" because to me it seemed fit. I then had to use quotation marks though because my translation otherwise would have become even harder to understand. I though that if I really wanted to make this a smooth translation with the understanding of the sentence I had so far, I would have to make huge changes to the english equivalent. Since I still was very skeptical if my basic understanding of the full sentence was correct at all, I decided against it.