The problem is that the method that you use and the paper referenced (https://pdfs.semanticscholar.org/ebf2/48c9fc0a1a23d1778b9408...) only applies the calculation on data 3 weeks, 4 weeks and 5 weeks after the epidemic has peaked. Of course you can get valid data once things have peaked and are slowing down. The issue is trying to get valid data while still in the exponential growth portion. And it seems like this method would have all the same flaws as other methods on rapidly changing data (if not worse due to the lag between recovery and deaths.).

I'm not an epidemiologist, but I believe I see flaws in your application of the methods from the paper.

[1] At the bottom page 481 it clearly say the virus peaked on March 27th. The first date they use data for the e2 calculation is April 6th. Two full weeks past the peak.