The unparalleled precision of recent experiments such as Planck have allowed us to constrain standard and non-standard physics (e.g. due to dark matter annihilation or varying fundamental constants) during the recombination epoch. However, we can also probe this era of cosmic history using model-independent variations of the free electron fraction, Xe, which, in turn, affects the temperature and polarization anisotropies of the cosmic microwave background. In this paper, we improve on the previous efforts to construct and constrain these generalized perturbations in the ionization history, deriving new optimized eigenmodes based on the full Planck 2015 likelihood data, introducing the new module FEAREC++. We develop a direct likelihood sampling method for attaining the numerical derivatives of the standard and non-standard parameters, and discuss complications arising from the stability of the likelihood code. We improve the amplitude constraints of the Planck 2015 principal components constructed here, μ1 = −0.09 ± 0.12, μ2 = −0.17 ± 0.20, and μ3 = −0.30 ± 0.35, finding no indication for departures from the standard recombination scenario. The error constraint on the third mode has been improved by a factor of 2.5. We utilize an efficient eigenanalyser that keeps the cross-correlations of the first three eigenmodes to Corr(μμ′)<0.1 per cent after marginalization for all the considered data combinations. We also propose a new projection method for estimating constraints on the parameters of non-standard recombination scenarios. As an example, using our eigenmode measurements, this allows us to recreate the Planck constraint on the two-photon decay rate, A2s1s = 7.60 ± 0.64, giving an error estimate to within ≃ 0.05σ of the full MCMC result. The improvements on the eigenmode analysis using the Planck data will allow us to implement this new method for analysis with fundamental constant variations in the future.