The awkward truth may be the part the smooth story needed.

A story sanded down until nothing catches is easy to tell and easy to forget. The rough part, the bit you would rather leave out, is usually where the account becomes believable and where someone else finds their own situation. Polish protects you; the awkward detail is what actually helps the listener. Leaving it out often costs more than saying it would.

Pick one account you tell often and notice the moment you always skip. Next time it comes up, try including it plainly, without apology or a long explanation. Watch what the room does with it.