“To make a long story short…”, does not mean the same thing as, “…and in summary”.
If you’re going to tell an entire story, and then sum it up, you just say, “…and in summary”. Please don’t try to fool the listener into thinking that telling your story twice – first the long version and then the short version – is making a long thing shorter. It’s actually making a long thing even longer.
So maybe change it to, “To make a long story longer…”, cause that’s really what you are saying. And hey, I just heard your whole story, so I don’t need to also hear the Cliffs Notes version.
That is all.