  The factorization and resummation approach of Nagar and Shah~[Phys.~Rev.~D~94
(2016), 104017], designed to improve the strong-field behavior of the
post-Newtonian (PN) residual waveform amplitudes $f_{\ell m}$'s entering the
effective-one-body, circularized, gravitational waveform for spinning
coalescing binaries, is here improved and generalized to all multipoles up to
$\ell=6$. For a test-particle orbiting a Kerr black hole, each multipolar
amplitude is truncated at relative 6~post Newtonian (PN) order, both for the
orbital (nonspinning) and spin factors. By taking a certain Pad\'e approximant
(typically the $P^4_2$ one) of the orbital factor in conjuction with the
inverse Taylor (iResum) representation of the spin factor, it is possible to
push the analytical/numerical agreement of the energy fluxe at the level of
$5\%$ at the last-stable-orbit for a quasi-maximally spinning black hole with
dimensionless spin parameter $+0.99$. When the procedure is generalized to
comparable-mass binaries, each orbital factor is kept at relative $3^{+3}$PN
order, i.e. the 3PN comparable-mass terms are hybridized with higher PN
test-particle terms up to 6PN relative order. The same Pad\'e resummation is
used for continuity. By contrast, the spin factor is only kept at the highest
comparable-mass PN-order currently available. We illustrate that the
consistency between different truncations in the spin content of the waveform
amplitudes is stronger in the resummed case than when using the standard
Taylor-expanded form of Pan et al.~[Phys.~Rev.~D~83 (2011) 064003]. We finally
introduce a method to consistently hybridize comparable-mass and test-particle
information {\it also} in the presence of spin (including the spin of the
particle), discussing it explicitly for the $\ell=m=2$ spin-orbit and
spin-square terms.
