  We study whether the universal runaway behaviour of stringy scalar potentials
towards infinite field distance limits can produce an accelerated expanding
cosmology \`{a} la quintessence. We identify a loophole to some proposed bounds
that forbid such asymptotic (at parametric control) accelerated expansion in 4d
$\mathcal{N}=1$ supergravities, by considering several terms of the potential
competing asymptotically. We then analyse concrete string theory examples
coming from F-theory flux compactifications on Calabi-Yau fourfolds, extending
previous results by going beyond weak string coupling to different infinite
distance limits in the complex structure moduli space. We find some potential
candidates to yield asymptotic accelerated expansion with a flux potential
satisfying $\gamma=\frac{\|\nabla V\|}{V}<\sqrt{2}$ along its gradient flow.
However, whether this truly describes an accelerated expanding cosmology
remains as an open question until full moduli stabilization including the
Kahler moduli is studied. Finally, we also reformulate the condition for
forbidding asymptotic accelerated expansion as a convex hull de Sitter
conjecture which resembles a convex hull scalar WGC for the membranes
generating the flux potential. This provides a pictorial way to quickly
determine the asymptotic gradient flow trajectory in multi-moduli setups and
the value of $\gamma$ along it.
