  Effective-one-body (EOB) models are based on analytical building blocks that,
mathematically, are truncated Taylor series with logarithms. These polynomials
are usually resummed using Pad\'e approximants obtained first assuming that the
logarithms are constant, and then replacing them back into the resulting
rational functions. A recent study pointed out that this procedure introduces
spurious logarithmic terms when the resummed functions are reexpanded. We
therefore explore analytically more consistent resummation schemes. Here we
update the TEOBResumS-Dali waveform model for spin-aligned, noncircularized,
coalescing black hole binaries by systematically implementing new (still Pad\'e
based) resummations for all EOB functions. Once the model is informed by 51
Numerical Relativity simulations this new approach proves key in lowering the
maximum EOB/NR unfaithfulness $\bar{F}_{\rm EOBNR}^{\rm max}$ for the
$\ell=m=2$ mode (with the Advanced LIGO noise in the total mass range
$10-200M_{\odot}$) over the whole Simulating eXtreme Spacetimes catalog of 534
waveforms. A median mismatch of $3.418\times 10^{-4}$ is achieved, which is a
marked improvement on the previous value, $1.06\times 10^{-3}$. The largest
value, $\bar{\cal F}^{\rm max}_{\rm EOBNR}\sim 10^{-2}$, is found for an
equal-mass, equal-spin simulation with dimensionless spins $\sim +0.994$; only
six configurations (all equal-mass, and with equal spins larger than $+0.97$)
are above $5\times 10^{-3}$. Results for eccentric binaries are similarly
excellent (well below $10^{-2}$ and mostly around $10^{-3}$). For scattering
configurations, we find an unprecedented EOB/NR agreement ($<1\%$) for
relatively small values of the scattering angle, though differences
progressively increase as the threshold of immediate capture is approached.
