Continental flood basalts intruded and erupted millions of km$^3$ of magma over $\sim$ 1-5 Ma. Previous work proposed the presence of large ($>$ 10$^5$-10$^6$ km$^3$) crustal magma reservoirs to feed these eruptions. However, in Paper I, we illustrated that this model is inconsistent with observations, by combining eruptive rate constraints with geochemical and geophysical observations from the Deccan Traps and other CFBs. Here, we use a new mechanical magma reservoir model to calculate the variation of eruptive fluxes (km$^3$/year) and volumes for different magmatic architectures. We find that a single magma reservoir cannot explain the eruptive rate and duration constraints for CFBs. Using a 1D thermal model and characteristic timescales for magma reservoirs, we conclude that CFB eruptions were likely fed by a number of interconnected small-medium ($\sim$ 10$^2$ - 10$^{3.5}$ km$^3$) magma reservoirs. It is unlikely that each individual magma reservoir participated in every eruption, thus permitting the occasional formation of large xenocrysts (e.g., megacrystic plagioclase). This magmatic architecture permits (a) large volume eruptive episodes with 10s to 100s of years duration, and (b) relatively short time-periods separating eruptive episodes (1000s of years) since multiple mechanisms can trigger eruptions (via magma recharge or volatile exsolution, as opposed to long term (10$^5$ - 10$^6$ year) accumulation of buoyancy overpressure); (c) lack of large upper-crustal intrusive bodies in various geophysical datasets. Our new proposed magmatic architecture has significant implications for the tempo of CFB volatile release (CO$_2$ and SO$_2$), potentially helping explain the pre-K-Pg warming associated with Deccan Traps.