[When it is at the Sun's surface,
the pull of the Sun's gravity on
the ping-pong ball will be at its
maximum.]

The instant the ping-pong ball plunges
past the surface of the Sun, the pull of
the Sun's gravity on the ping-pong ball
will begin to decrease.

OK


Actually, this is not generally true and hence not "OK". It is always true
if the body has constant density, but the Sun doesn't. It may also be true
for the Sun, as long as you are careful about where you define the surface
of the Sun to be, but cannot just be assumed to be true.

I can certainly give you mass distributions which are spherically symmetric
but for which gravity is higher underground than on the surface. As an
extreme example imagine the Sun had a black hole the size of a grain of sand
at its centre. The gravity near the surface of that grain of sand would far
exceed that on the surface of the Sun. Not that black holes are needed for a
counter example - the object just needs much higher densities at its core
than it has on the surface.

Not that this in any way affects the validity of your argument.