  Direct collapse black holes~(BH) are promising candidates for producing
massive $z\gtrsim 6$ quasars, but their formation requires fine-tuned
conditions. In this work, we use cosmological zoom simulations to study
systematically the impact of requiring: 1) low gas angular momentum, and 2) a
minimum incident Lyman-Werner~(LW) flux in order to form BH seeds. We probe the
formation of seeds (with initial masses of $M_{\rm seed} \sim 10^4$ - $10^6
M_{\odot}/h)$ in halos with a total mass $> 3000\times M_{\mathrm{seed}}$ and a
dense, metal poor gas mass $> 5\times M_{\mathrm{seed}}$. We find that the
seed-forming halos have a prior history of star formation and metal enrichment,
but contain pockets of dense, metal poor gas. When seeding is further
restricted to halos with low gas spins, the number of seeds formed is
suppressed by factors of $\sim6$ compared to the baseline model, regardless of
the seed mass. Seed formation is much more strongly impacted if the dense,
metal poor gas is required to have a critical LW flux ($J_{\mathrm{crit}}$).
Even for $J_{\mathrm{crit}}$ values as low as $50J_{21}$, no
$8\times10^{5}M_{\odot}/h$ seeds are formed. While lower mass
($1.25\times10^{4},1\times10^{5} M_{\odot}/h$) seeds do form, they are strongly
suppressed~(by factors of $\sim10-100$) compared to the baseline model at gas
mass resolutions of $\sim10^4~M_{\odot}/h$ (with even stronger suppression at
higher resolutions). As a result, BH merger rates are also similarly
suppressed. Since early BH growth is dominated by mergers in our models, no
seeds are able to grow to the supermassive regime~($\gtrsim10^6 M_{\odot}/h$)
by $z=7$. Our results hint that producing the bulk of the $z\gtrsim6$
supermassive BH population may require alternate seeding scenarios that do not
depend on the LW flux, early BH growth dominated by rapid or super-Eddington
accretion, or a combination of these possibilities.
