First and foremost, all three of those sentences are correct. The differences are very, very miniscule between the meaning. Someone might come along and point out some tiny connotative difference, but none come to mind right now for me - in any case that I can imagine using one of those, I can exchange it with any of the other two options and the meaning stays the same.
I'll comment here that I think this would be a better sentence to express what you're trying to saying:
That day was the most romantic day of my life.
That _______ (event) was the most romantic thing that has ever happened to me.
The way you currently have it, you're saying that the "day" is a "romantic thing" that happened to you. And days aren't things, and they don't happen to you. For that reason, I think one of the two options above is better.
As for the verbs that you can use, all three examples are grammatically correct and have extremely similar meanings, so it's up to you!
EDIT: I did manage to come up with one tiny difference between the three!
In the case of the first sentence,
That day was the most romantic thing that had ever happened to me.
You COULD potentially follow up with
Until today's candelit dinner! Today was so romantic - certainly the most romantic thing that has ever happened to be.
Because you have "had" there (in the past tense), we can clarify that things are different now if we want. However, on it's own (without the second quote), in that use, I don't think that "had ever happened to me" implies on its own that the event was surpassed.
The other two sentences couldn't be switched in here, as they use "has," which is in the present, and so makes it clear that the one romantic event still takes the cake.