Holy technical question, batman!

I have no idea what the actual law is on the subject.  I'll ask next time I see somebody who does.

But, in the meantime, I will speculate and observe.

The real answer, of course, is "no".  It doesn't matter what the words on the page say.  Just like the looniebins suing the IRS on grounds that the income tax is unconstitutional, any claim that Congress could casually legislate the Court out of business would be declared invalid, just because.  You may have a fine technical argument, but you would simply not be allowed to completely overturn our governmental structure on a technicality.

The Constitution would be read to mean what it needed to mean to maintain the status quo, more or less.  And who do you think is in charge of interpreting the constitution, hmm?  Notice how the Court bent and twisted the second amendment to basically arrive at "current practice is ok" in the DC case.  The Court rarely does anything that leads to major upheaval, and certainly would not rule anything this massive.

On a more substantive level, I think you are reading it wrong.  I read that sentence to mean that Congress has the ability to rearrange whether the Court has original or appellate jurisdiction.  The question of whether there is Federal jurisdiction at all is mentioned elsewhere, and not subject to this qualifier.