  Measuring the Higgs trilinear self-coupling $\lambda_{hhh}$ is experimentally
demanding but fundamental for understanding the shape of the Higgs potential.
We present a comprehensive analysis strategy for the HL-LHC using di-Higgs
events in the four $b$-quark channel ($hh \to 4b$), extending current methods
in several directions. We perform deep learning to suppress the formidable
multijet background with dedicated optimisation for BSM $\lambda_{hhh}$
scenarios. We compare the $\lambda_{hhh}$ constraining power of events using
different multiplicities of large radius jets with a two-prong structure that
reconstruct boosted $h \to bb$ decays. We show that current uncertainties in
the SM top Yukawa coupling $y_t$ can modify $\lambda_{hhh}$ constraints by
$\sim 20\%$. For SM $y_t$, we find prospects of $-0.8 < \lambda_{hhh} /
\lambda_{hhh}^\text{SM} < 6.6$ at 68% CL under simplified assumptions for
3000~fb$^{-1}$ of HL-LHC data. Our results provide a careful assessment of
di-Higgs identification and machine learning techniques for all-hadronic
measurements of the Higgs self-coupling and sharpens the requirements for
future improvement.
