Isn't a "progressive" income tax short of that mark [uniform ]?
Yes, it does. But, an amendment is considered to supersede any conflicting statements that precede it in either the original document or in prior amendments. That's why the 17th Amendment, relating to the election of Senators, is considered to have superseded Article 1, Section 3, of the Constitution (in the news this week).
The 16th Amendment is considered to have superseded part of Article 1, Section 9, of the Constitution, in particular, the phrase:
"No Capitation, or other direct, Tax shall be laid, unless in Proportion to the Census or enumeration herein before directed to be taken."
To read the Constitution and Amendments and see what each Amendment changed, see the Constitutional Issues section of the Action America web site. Start with the Constitution. Wherever you see a link in the text of the Constitution or any Amendment, the linked text is superseded by the Amendment that the link points to.
I hope that this helps.