Before I get into this, let me first point out that it's, as always, a
futile argument.  We'll all have different opinions on the matter and
that isn't likely to change.

That being said...

>Can anyone beat that?

Yes.

> 1.  Have a lasting influence on the course of music.

Stravinsky.

> 2.  Be proficient in all genres of his day.

Certainly.  Composed (just off the top of my head) symphonys, ballets,
operas, oratorios, liturgical works, concertos, choral works, vocal
works, sonatas, chamber music, works for unaccompanied instruments,
and even works for wind band and jazz band.  Beat that, Tchaikovsky.

> 3.  Show a wide expressive range.

I think so.

> 4.  A consistency of result.  Not everything must be wonderful,
> but a preponderance should.

It all sounds like Stravinsky.  Even the really early stuff (Symphony
in Eb) and late stuff (Aldous Huxley Variations)

> 5.  I'm not as sure about this one, but at least one semi-popular
> hit.  To me, this shows that the music speaks to everybody.

Firebird? The Rite of Spring?

> Stravinsky - weak chamber output.  His influence has waned.

Weak chamber output?  What about Soldiers Tale?  Octet?  It wasn't the
area of his largest output, but I think it is more than made up for by
the amount of music he wrote in other genres.

As for his influence: go to any college level composition program and
ask the students (and faculty) who their biggest influences are.  The
names you will likely hear most will be Ligeti, Bartok, and Stravinsky.
Furthermore, you'd have a difficult time finding a serious classical
musician who can't tell you the exact day and time that they first heard
The Rite of Spring.  By the criteria presented, I think Stravinsky wins.

-Nathan L.