Below a first attempt using the years 1983-2005 (BP data), the peak year is 2013:



Not to make too much of this, but eyeballing the graph the 2013 predicted peak looks like around 1.5 mbpd more than now?
+2.53 mbpd to be precise:

P(2013)= 83.62 mbpd
P(2005)= 81.1 mbpd

Just a reminder to all that this would indicate an 88-mbd peak (83.6 + 4.4 ref gain) based on ASPO.
Actually, BP & ASPO differ on 2005.  The indicated all liquids peak is implied at 86.7-mbd (83.6 + 3.1 ref gain) based on BP/IEA data for 2005.
The problem with all linearizations is choosing which data to include in the fit. Depending on your data choice you can move the peak around a few years.
Thats why it would be nice to have a method where you didn't have to exclude any data points.  The 2nd HL method looks closer to being able to do that.
I agree, it'a common problem with the curve fitting approach especially when we have several production peaks.