Thanks for writing to JustAnswer.
I see that you want to find a way to tell her,"thanks, XXXXX XXXXX but maybe later." May I suggest that you re-think this?
If you want to perhaps someday be in a relationship with her, do you really want her to think you are the kind of guy who is lining up his next relationship while he's still in a committed relationship? Most women would take this as a red flag.
There seems to be a lot of mental energy being spent on what was essentially a friendship, which has apparently now cooled (with her giving you the cold shoulder).
She could have seen you as a safe friend, as you are also in a relationship. Her playing with her hair could be a nervous habit. If your conversation never delved into your private lives, the chances are good that she liked you as a friend, but had no further intentions. You changing the dynamic by acting "warm, but aloof" would be very confusing to her if that were the case. You worrying that her self esteem would be affected by something you say is a bit premature...especially since she's seeing someone.
This is not what you wanted to hear, but it seems like you're trying to have your cake and eat it too... You're in a relationship, she's in a relationship. There is no "thing" to be ended on a happy note. You had a casual work friendship until you started reading body language and I think there's a good chance you read it wrongly. The fact that she didn't "elevate the flirting to a higher level" could also mean that she has good boundaries and doesn't believe in flirting when she's involved with someone, or when she's talking with someone who's in a relationship.
I'm sure this is not what you wanted to hear, but I think the chance of you embarrassing yourself by making an issue of this is too risky. And because this is a co-worker, you might leave yourself open to a sexual harassment complaint. She has backed off from the friendship...this is not the time to be stirring things up.
This is one time when doing nothing is truly your best course of action.