  Within a simple quantization scheme, observables for a large class of finite
dimensional time reparametrization invariant systems may be constructed by
integration over the manifold of time labels. This procedure is shown to
produce a complete set of densely defined operators on a physical Hilbert space
for which an inner product is identified and to provide reasonable results for
simple test cases. Furthermore, many of these observables have a clear
interpretation in the classical limit and we use this to demonstrate that, for
a class of minisuperspace models including LRS Bianchi IX and the
Kantowski-Sachs model this quantization agrees with classical physics in
predicting that such spacetimes recollapse.
