  Understanding large-scale magnetic field growth in astrophysical objects is a
persistent challenge. We tackle the long-standing question of how much helical
large-scale dynamo growth occurs independent of the magnetic Reynolds number
(Rm) in a closed volume. From modest-Rm numerical simulations, we identify a
pre-saturation regime when the large-scale field grows independently of Rm, but
to an Rm-dependent magnitude. For plausible magnetic spectra however, the
analysis predicts the magnitude to be Rm-independent and substantial as
Rm$\to\infty$. This gives renewed optimism for the relevance of closed dynamos
and pinpoints how modest Rm and hyper-diffusive simulations can cause
misapprehension of the Rm$\to\infty$ behavior.
