  The complex phase diagram of manganites with simultaneously active spin,
charge, orbital, and lattice degrees of freedom continues providing surprises.
In a recent groundbreaking experiment, membranes of the perovskite manganite
La$_{0.7}$Ca$_{0.3}$MnO$_3$ (LCMO) deposited on a flexible polymer layer were
strained up to 8\% [S.~S. Hong {\it et al.}, Science {\bf 368}, 71 (2020)],
much more than achieved by regular strain induced by a rigid substrate. By
increasing this strain a metal-insulator transition was reported. Here we
reproduce the results of the experiments using Monte Carlo simulations of the
two-orbital double-exchange model including Jahn-Teller distortions, at hole
density $x=1/3$. The full phase diagram with varying temperature and
Jahn-Teller coupling $\lambda$ is presented. When the bandwidth $W$ of mobile
electrons is reduced, thus when the effective Jahn-Teller coupling $\lambda/W$
is increased, a metal-insulator transition is found in our simulations, between
a ferromagnetic metallic state with uniform charge distribution and an
insulator with diagonal charge stripes that retains its ferromagnetic
character. In between the hole-rich diagonals, staggered orbital order occurs.
We also report resistivity and magnetization measurements alongside with spin
correlations and charge structure factors. Our overall conclusions are in
agreement with the recent experimental and density functional theory results by
Hong {\it et al.}, and we confirm much earlier ground state predictions of
striped ferromagnetic order using energy optimization techniques by T. Hotta
{\it et al.}, Phys. Rev. Lett. {\bf 86}, 4922 (2001). The experimental
observation of one of the states predicted by theory suggests that diagonal
stripes could be achieved at other hole densities as well, such as $x=1/4$, if
LCMO membranes with that hole doping were subject to similar strains.
