The use of effective-one-body (EOB) waveforms for black hole binaries analysis in gravitational-wave astronomy requires faithful models and fast generation times. A key aspect to achieve faithfulness is the inclusion of numerical-relativity (NR) informed next-to-quasicircular corrections(NQC), dependent on the radial momentum, to the waveform and radiation reaction. A robust method to speed up the waveform generation is the post-adiabatic iteration to approximate the solution of the EOB Hamiltonian equations. In this work, we assess the performances of a fast NQC prescription in combination to the post-adiabatic method for generating multipolar gravitational waves. The outlined approach allows a consistent treatment of NQC in both the waveform and the radiation-reaction, does not require iterative procedures to achieve high faithfulness, and can be efficiently employed for parameter estimation. Comparing to 611 NR simulations, for total mass $10M_odotleq M leq 200M_odot$ and using the Advanded LIGO noise, the model has EOB/NR unfaithfulness well below $0.01$, with 78.5% of the cases below $0.001$. We apply the model to the parameter estimation of GW150914 exploring the impact of the new NQC and of the higher modes up to $ell=m=8$.
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