  We apply a continuation method to recently optimized stellarator equilibria
with excellent quasi-axisymmetry (QA) to generate new equilibria with a wide
range of rotational transform profiles. Using these equilibria, we investigate
how the rotational transform affects fast-particle confinement, the maximum
coil-plasma distance, the maximum growth rate in linear gyrokinetic
ion-temperature gradient (ITG) simulations, and the ion heat flux in
corresponding nonlinear simulations. We find values of two-term quasisymmetry
error comparable to or lower than the similar Landreman-Paul (Phys. Rev. Lett.
128, 035001) configuration for values of the mean rotational transform
$\bar{\iota}$ between $0.12$ and $0.75$. The fast-particle confinement improves
with $\bar{\iota}$ until $\bar{\iota} = 0.73$, at which point the degradation
in quasisymmetry outweighs the benefits of further increasing $\bar{\iota}$.
The required coil-plasma distance only varies by about $\pm 10\%$ for the
configurations under consideration, and is between $2.8\,\mathrm{m}$ to
$3.3\,\mathrm{m}$ when the configuration is scaled up to reactor size. The
maximum growth rate from linear gyrokinetic simulations increases with
$\bar{\iota}$, but also shifts towards higher $k_y$ values. The maximum linear
growth rate is sensitive to the choice of flux tube at rational $\iota$, but
this can be compensated for by taking the maximum over several flux tubes. The
corresponding ion heat fluxes from nonlinear simulations display a
non-monotonic relation to $\iota$. Sufficiently large positive shear is
destabilizing. This is reflected both in linear growth rates and nonlinear heat
fluxes.
