in NYC, employers aren't allowed to ask for past salary data
Not just NYC.
New York Labor Law section 194-a states that "No employer shall . . . b. orally or in writing seek, request, or require the wage or salary history from an applicant or current employee as a condition to be interviewed, or as a condition of continuing to be considered for an offer of employment, or as a condition of employment or promotion."
many simply dodge around the question by asking how much would you like to make
I'm curious how you purport to know what "many" NYC employers do. Have you collected survey data?
and obviously that's typically 10-20% over what you currently make in most cases with tenured professionals.
I don't think that's obvious at all, but I guess what you're suggesting is that "many" employers ask how much an applicant wants to make and then divides the response by 1.1 or 1.2 to estimate the applicant's prior salary. Is that what you're suggesting?
If you accidentally slip some data around what your W2-'s have looked like,
I have no idea what this means.
can the new employer verify salary data or W-2 data from any 3rd party companies before you join them?
As noted above, section 194-a makes it illegal for an employer to "seek" an applicant's wage or salary history. However, section 194-a(2) states that "Nothing in this section shall prevent an applicant or current employee from voluntarily, and without prompting, disclosing or verifying wage or salary history, including but not limited to for the purposes of negotiating wages or salary."
Well to negotiate, you have to have some basis and some background.
Who is "you" in this sentence?
I can't randomly throw a number and let it stick in my world.
Huh?
given this company will use a 3rd party background check company, what should I provide them to say I was employed by x company?
As phrased, this question raises no legal issue. A prospective employer hiring an upper level employee will be specific with what it requests if it need additional information to run background checks.