Joachim,
all good work, but don't you think the biggest problem with the CAPE is the first assumption that everyone forgets

assumption 1. use 10 years of historic earnings so as to approximate a business cycle

... the reason you are trying to capture a full business cycle is then you capture the peaks and troughs of the cycle .. hence the name, cyclically adjusted PE.
problem is the real world didn't get the memo about the 10 year assumption. Business cycles are of varying length. To offset peak period earnings you need a trough. So some 10 year periods capture just one peak and one trough, other 10 year periods may have two peaks and one trough or two troughs one peak etc ... all of this then makes for a very blunt indicator

So in concept, CAPE is good ... but in practice the period it is calculated over needs to be aligned to business cycles and this means any rolling 10 year period creates a nonsense. that is why it has very little predictive value other than the bluntness of high markets (and hence almost any accounting indicator) due to mean reversion of capitalism, means lower forward returns.

using a 5 year period would likely miss a full business cycle - so refutes the cyclically adjusted part of the name.

So a long slow expansion will result in a high CAPE, simply because earnings weren't 're-based' from recessions. Equally double dip downturns end up producing artificially low CAPEs
the fact is, leading into a bear market (which is when you want the predictor to predict) the CAPE has been anywhere from 7 to 44 !! Just before the dotcom crash, the CAPE was 44. Just before the 1981/82 deep recession it was only 9.

Please tell me what is the correct level of CAPE to sell my investments on - in advance of the downturn please, I'm struggling to see it clearly.

predictive indicators are only as good as their ability to enable you to predict.

all the best
john