You can say "제가 말하고자 하는 것은-" when you want to repeat/emphasize/encapsulate the point of what you have just said. For example, if you diversed in the middle of conversation, you think you didn't deliver the point of what you were talking about, or someone suddenly interfered and changed the subject etc. It functions as an introduction of what you want to say. And it's rather formal. It seems perfectly natural to me. :)

Could you be more specific? ^^' Actually I am still figuring out what you want to know about. "제가 말하려고 하는 것은.." can mean "what I am trying to say is..." or "what I am going to say..." not "what I wanted to say was...(=제가 말하려고 했던것은)". This style is often found in speeches or presentations to introduce or emphasize a topic. We often say "(그러니까) 내(제) 말(씀)은..." in a daily conversation. \^o^/