  We study the non-equilibrium dynamics of the spherical ferromagnet quenched
to its critical temperature, as a function of the magnetization of the initial
state. The two limits of unmagnetized and fully magnetized initial conditions
can be understood as corresponding to times that are respectively much shorter
and much longer than a magnetization timescale, as in a recent field
theoretical analysis of the $n$-vector model. We calculate exactly the
crossover functions interpolating between these two limits, for the
magnetization correlator and response and the resulting fluctuation-dissipation
ratio (FDR). For $d>4$ our results match those obtained recently from a
Gaussian field theory. For $d<4$, non-Gaussian fuctuations arising from the
spherical constraint need to be accounted for. We extend our framework from the
fully magnetized case to achieve this, providing an exact solution for the
relevant integral kernel. The resulting crossover behaviour is very rich, with
the asymptotic FDR $X^\infty$ depending non-monotonically on the scaled age of
the system. This is traced back to non-monotonicities of the two-time
correlator, themselves the consequence of large magnetization fluctuations on
the crossover timescale. We correct a trivial error in our earlier calculation
for fully magnetized initial states; the corrected FDR is {\em consistent} with
renormalization group expansions to first order in $4-d$ for the longitudinal
fluctuations of the O(n) model in the limit $n\to\infty$.
