In a recent paper we found evidence for an increase in the accretion rate during photospheric radius expansion bursts, quantified by a variable normalization factor fa on the preburst persistent emission. Here we follow this result up on a much larger sample of 1759 type I X-ray bursts from 56 sources. We show that the variable persistent flux method provides improvements in the quality of spectral fits for type I bursts, whether or not they reach the Eddington luminosity. The new approach has an estimated Bayes factor of 64 improvement over the standard method, and we recommend that the procedure be adopted as standard for analyzing type I bursts. We show evidence that the remaining discrepancies to a formally consistent spectral model are due to the burst component deviating significantly from a blackbody, rather than variations in the spectral shape of the persistent emission component. In bursts that do not show radius expansion, the persistent emission enhancement does not exceed 37% of the Eddington flux. We use this observation to constrain the Eddington flux of sources for which FEdd has not been directly measured.