I did a similar calculation but came back more optimistically (although still on scale of a year to two).

You only need count over 18s as very few cases in this group. It is believed by the UK experts to have a lower fatality rate of 1% and likely lower admission rate due to asymptomatic infections (estimates at 16-75%). Ventilator capacity can increase with stopping surgery and CPAP/other measures can be used in some cases. Treatments developed later should improve efficiency of treatment. Extra ventilators should be manufactured and help ease burden. I think 80% is too high, likely more 60% given an R0 of 2-3. Finally, the chronically unwel elderly are unlikely to benefit from ITU care significantly and would never qualify. With these exceptions it gets down to 1-2 years depending on assumptions.