Our limited understanding of millennial-scale variability in the context of the last glacial period can be explained by the lack of a reliable modelling framework to study abrupt climate changes under realistic glacial backgrounds. In this article, we describe a new set of long-run Last Glacial Maximum experiments where such climate shifts were triggered by different snapshots of ice-sheet meltwater derived from the early stages of the last deglaciation. Depending on the location and the magnitude of the forcing, we observe three distinct dynamical regimes and highlight a subtle window of opportunity where the climate can sustain oscillations between cold and warm modes. We identify the European-Arctic and Nordic Seas regions as being most sensitive to meltwater discharge in the context of switching to a cold mode, compared to freshwater fluxes from the Laurentide ice sheets. These cold climates follow a consistent pattern in temperature, sea ice and convection, and are largely independent from freshwater release as a result of effective AMOC collapse. Warm modes, on the other hand, show more complexity in their response to the regional pattern of the meltwater input, and within them, we observe significant differences linked to the reorganisation of deep water formation sites and the subpolar gyre. Broadly, the main characteristics of the oscillations, obtained under full-glacial conditions with realistically low meltwater discharge, are comparable to δ¹⁸O records of the last glacial period, although our simplified experiment design prevents detailed conclusions from being drawn on whether these represent actual Dansgaard-Oeschger events.