  We compute the transport and chaos properties of lattices of quantum
Sachdev-Ye-Kitaev islands coupled by single fermion hopping, and with the
islands coupled to a large number of local, low energy phonons. We find two
distinct regimes of linear-in-temperature ($T$) resistivity, and describe the
crossover between them. When the electron-phonon coupling is weak, we obtain
the `incoherent metal' regime, where there is near-maximal chaos with front
propagation at a butterfly velocity $v_B$, and the associated diffusivity
$D_{\rm chaos} = v_B^2/(2 \pi T)$ closely tracks the energy diffusivity. On the
other hand, when the electron-phonon coupling is strong, and the linear
resistivity is largely due to near-elastic scattering of electrons off nearly
free phonons, we find that the chaos is far from maximal and spreads
diffusively. We also describe the crossovers to low $T$ regimes where the
electronic quasiparticles are well defined.
