  The lensing signal around galaxy clusters can, in principle, be used to test
detailed predictions for their average mass profile from numerical simulations.
However, the intrinsic shape of the profiles can be smeared out when a sample
that spans a wide range of cluster masses is averaged in physical length units.
This effect especially conceals rapid changes in gradient such as the steep
drop associated with the splashback radius, a sharp edge corresponding to the
outermost caustic in accreting halos. We optimize the extraction of such local
features by scaling individual halo profiles to a number of spherical
overdensity radii, and apply this method to 16 X-ray-selected high-mass
clusters targeted in the Cluster Lensing And Supernova survey with Hubble. By
forward-modeling the weak- and strong-lensing data presented by Umetsu et al.,
we show that, regardless of the scaling overdensity, the projected ensemble
density profile is remarkably well described by an NFW or Einasto profile out
to $R \sim 2.5h^{-1}$Mpc, beyond which the profiles flatten. We constrain the
NFW concentration to $c_{200c} = 3.66 \pm 0.11$ at $M_{200c} \simeq 1.0 \times
10^{15}h^{-1}M_\odot$, consistent with and improved from previous work that
used conventionally stacked lensing profiles, and in excellent agreement with
theoretical expectations. Assuming the profile form of Diemer & Kravtsov and
generic priors calibrated from numerical simulations, we place a lower limit on
the splashback radius of the cluster halos, if it exists, of $R_{sp}/r_{200m} >
0.89$ ($R_{sp} > 1.83h^{-1}$Mpc) at 68% confidence. The corresponding density
feature is most pronounced when the cluster profiles are scaled by $r_{200m}$,
and smeared out when scaled to higher overdensities.
