We report the results of a CCD imaging survey, complemented by astrometric and spectroscopic follow-up studies, that aims to probe the fate of heavy-weight intermediate-mass stars by unearthing new, faint, white dwarf members of the rich, nearby, intermediate-age open clusters NGC 3532 and NGC 2287. We identify a total of four white dwarfs with distances, proper motions and cooling times which can be reconciled with membership of these populations. We find that WD J0643-203 in NGC 2287, with an estimated mass of M= 1.02-1.16 M&sun;, is potentially the most massive white dwarf so far identified within an open cluster. Guided by the predictions of modern theoretical models of the late-stage evolution of heavy-weight intermediate-mass stars, we conclude that there is a distinct possibility that it has a core composed of O and Ne. We also determine that despite the cooling times of the three new white dwarfs in NGC 3532 and the previously known degenerate member NGC 3532-10 spanning ˜90 Myr, they all have remarkably similar masses (M˜ 0.9-1 M&sun;). This is fully consistent with the results from our previous work on a heterogeneous sample of ˜50 white dwarfs from 12 stellar populations, on the basis of which we argued that the stellar initial-final mass relation is less steep at Minit > 4 M&sun; than in the adjacent lower initial mass regime. This change in the gradient of the relation could account for the secondary peak observed in the mass distribution of the field white dwarf population and mitigate the need to invoke close binary evolution to explain its existence. Spectroscopic investigation of numerous additional candidate white dwarf members of NGC 3532 unearthed by a recent independent study would be useful to confirm (or otherwise) these conclusions.