You may be right, KyJim. I haven't done a great deal of research on poll taxes in recent years. A quick SCOTUS search on Westlaw shows a number of cases invalidating poll taxes. Interestingly, none of the first few that I looked at (ranging from ca. 1965-75) said anything about the 15th Amendment, but rather the 14th and 24th Amendments, primarily the 24th. (I was approaching it from a 1st Amendment train of thought.) For those following along, the 24th Amendment says:
U.S. Const. amend. XXIV
Section 1. The right of citizens of the United States to vote in any primary or other election for President or Vice President, for electors for President or Vice President, or for Senator or Representative in Congress, shall not be denied or abridged by the United States or any State by reason of failure to pay any poll tax or other tax.
Section 2. The Congress shall have power to enforce this article by appropriate legislation.
So it looks like we have a more specific provision on poll taxes than the 15th. That's not to say that a proper plaintiff couldn't argue violations of both Amendments. Clearly, he or she could. While doing my admittedly brief research, I did find language that could be useful in an challenge to something like the NY fee structure:
Since, in general, only those who wish to vote pay the poll tax, the tax as administered by the State is equivalent to a charge or penalty imposed on the exercise of a fundamental right. If the tax were increased to a high degree, as it could be if valid, it would result in the destruction of the right to vote. . . .
It has long been established that a State may not impose a penalty upon those who exercise a right guaranteed by the Constitution. . . . ‘Constitutional rights would be of little value if they could be * * * indirectly denied,’ . . . . ‘manipulated out of existence,’ . . .
United States v. State of Tex., 252 F. Supp. 234, 254 (W.D. Tex. 1966) aff'd sub nom. Texas v. United States, 384 U.S. 155, 86 S. Ct. 1383, 16 L. Ed. 2d 434 (1966)(internal citations omitted by Spats for brevity)
In US v. State of Texas
the poll tax was a "voluntary" tax in that it was only paid by those who wished to vote. Texas took no other steps to enforce the tax. This is not so dissimilar from the NY fee situation that I would call the argument, that the NY fee is impermissible as a charge or penalty imposed on the exercise of a fundamental right, entirely untenable.