I don't think there's any way other than take a screenies of your current toon and match it up when you make the new one. Some things can be altered at the Barber but not all. Skin tone, heritage and body type cannot be altered afaik. Hair style, scars can be changed. Not sure if you can do a nose job though.
In SWTOR doing many beta runs, I took a screenies of the char creation page for my archives so that on resets I would know which sliders went where. It's probably too late for this in your case, but you might want one going forward.
fwiw: I too just created a toon to go to Landy events. But I like my toons to be "all different" otherwise I couldn't tell the apples from the oranges.
Whoever says “I” creates the “you.” Such is the trap of every conscience. The “I” signifies both solitude and rejection of solitude. Words name things and then replace them. Whoever says tomorrow, denies it. Tomorrow exists only for him who does not seek it. And yesterday? Yesterday is Kolvillàg: a name to forget, a word already forgotten.
The Oath: A Novel by Elie Wiesel