  The classification of 4D reflexive polytopes by Kreuzer and Skarke allows for
a systematic construction of Calabi-Yau hypersurfaces as fine, regular, star
triangulations (FRSTs). Until now, the vastness of this geometric landscape
remains largely unexplored. In this paper, we construct Calabi-Yau orientifolds
from holomorphic reflection involutions of such hypersurfaces with Hodge
numbers $h^{1,1}\leq 12$. In particular, we compute orientifold configurations
for all favourable FRSTs for $h^{1,1}\leq 7$, while randomly sampling
triangulations for each pair of Hodge numbers up to $h^{1,1}=12$. We find
explicit string compactifications on these orientifolded Calabi-Yaus for which
the D3-charge contribution coming from O$p$-planes grows linearly with the
number of complex structure and K\"ahler moduli. We further consider non-local
D7-tadpole cancellation through Whitney branes. We argue that this leads to a
significant enhancement of the total D3-tadpole as compared to conventional
$\mathrm{SO}(8)$ stacks with $(4+4)$ D7-branes on top of O7-planes. In
particular, before turning-on worldvolume fluxes, we find that the largest
D3-tadpole in this class occurs for Calabi-Yau threefolds with
$(h^{1,1}_{+},h^{1,2}_{-})=(11,491)$ with D3-brane charges
$|Q_{\text{D3}}|=504$ for the local D7 case and $|Q_{\text{D3}}|=6,664$ for the
non-local Whitney branes case, which appears to be large enough to cancel
tadpoles and allow fluxes to stabilise all complex structure moduli. Our data
is publicly available under
http://github.com/AndreasSchachner/CY_Orientifold_database .
