@AC: "If you read the actual academic article..."
I have. I admit I just read it and I did not go into the details of the Parallel Ice Sheet Model or the GENIE Earth system model (I once looked into that to the extent of the open literature, but I assume there have been significant advances since). So I can't review the methodology, which I would do if I were doing a peer review. I will offer some observations to those who cannot be bothered.
1. I do not see Lewis making any misrepresentations. He takes just one aspect of the results, and not the main one from the authors' PoV, but his understanding of that aspect is correct. Lewis, the authors of the paper, and IPCC (I mentioned that in an earlier and shorter post) all agree - imagine that! Kudos to Lewis for digging into "supplementary data" - the main paper does not deal with such small scales - a mere century is not worth much attention, after all.
2. The larger scale (think millennia) Fig 3 provides an interesting reference number: "Between 2010 and 2014, there has been an increase in cumulative emissions of about 40 GtC." [GtC stands for Gigatonne of Carbon - TFMR]. That's about 8GtC/yr during these last 5 years (NB: there isn't much history of anthropogenic carbon emissions). The authors then run a range of models that go up to 80GtC/yr at peak. The burn rate is not uniform, but they assume that within 500 years we will have nothing to burn, anyway (this is me being Lewis-y, apart from the 500 years figure that comes from the paper). To their credit the post-2010 cumulative emissions cover a wide range - they don't just focus on the worst-case scenario.
3. They make assumptions that the effect will last tens of thousands of years. I can't say without further reading how well-justified the assumption is. The justification is based on another assumption that if you pump a lot of CO2 into the atmosphere the mitigating effect of the oceans will be weaker than what is observed. I seriously doubt we know enough of the relevant properties of our oceans to state this as a fact. I suspect it is a result of some other (uncertain) model, but I cannot state that as a fact. I also don't know whether the models take into account, e.g., that the resulting carbon will block sunlight sufficiently to reduce warming (don't be surprised, such things are often omitted).
4. In any case, they have a very short observation period to get any input for their models, or to estimate parameters. They extrapolate their results to many millennia though. Under their assumptions and models, if you keep pumping 8GtC/yr on average for 500 years (that's 4000GtC cumulative emissions in their parametrisation), the Antarctic will lose a significant proportion of ice, and the sea level will be rising at a rate of ~2m/century for the 1st millennium from now, and slower after that (this is from the same Fig 3 mentioned above). Given that fossil fuels have been in use for a lot less than 500 years and there is no reason to assume they will remain our main source of energy for that long, I am not terribly worried.
5. This extrapolation does not make the paper completely useless academically, far from that. It should not, however, support any "We are DOOMED, I tell you!!!" screams or used to justify any spending of taxpayers' money beyond research grants that are a drop in the ocean (pardon the pun) anyway.