  We assess the consistency of cosmological models that alter the size of the
sound horizon at last scattering to resolve the Hubble tension with data from
ACT + Planck CMB lensing, Big Bang Nucleosynthesis, and supernova data from
Pantheon or Pantheon+. We use early dark energy (EDE) as an example model but
conclude that the results apply to other similar models. We constrain
$\Lambda$CDM and EDE with these data finding that while they can constrain
$\Lambda$CDM very tightly, EDE opens up the parameter space significantly and
allows $H_0 > 72$ km s$^{-1}$ Mpc$^{-1}$. We combine these data with
measurements from ACT + Planck TT650TEEE CMB primary anisotropy and galaxy
baryon acoustic oscillations, and find that overall, EDE fits these data better
than $\Lambda$CDM at $\approx 2\sigma$. However, the fit to specifically the
sound-horizon-independent measurements is worse for EDE than $\Lambda$CDM. We
assess this increase in $\chi^2$ coming from the sound-horizon-independent
measurements and find that the best-fit model is still consistent with a random
statistical fluctuation even with $H_0$ values around $72$ km s$^{-1}$
Mpc$^{-1}$. We conclude that these specific sound-horizon-independent data
cannot rule out the possibility of a miscalibration of the size of the sound
horizon, but leave open the possibility that other current or future
sound-horizon-independent data sets could rule out such a miscalibration.
