Having been enlightened by knowledgeable replies, let me re-state the
problem.

Instead of points 2 & 3 being perfectly fixed points, let them be
springs, with equal spring constants. So the forces will be
proportional to the deflections at those points. If I still assume a
perfectly rigid lever, then the deflections will be proportional to the
distances and it's solvable (statically determinable, if that's the way
it's put).

If A (alpha) is the angular deflection and k is the spring constant then:

F2 = k * L2 * sinA (for really small A)
F3 = k * L3 * sinA
and F2 = F3*L2/L3
etc

Which is exactly opposite of my original intuition that the forces would
be _inversely_ proportional to the distance.

As k gets really large (and A small, but k * sinA finite, it starts to
look like my original problem of points 2 & 3 fixed. But I suppose that
the limit of k*sinA is not determinate and it's not _exactly_ the same case.

I await your destruction of my "thesis",
Bob