I'm glad to know you found it helpful!
The answer is no. One cannot tell just from the shift pattern whether it is Doppler from local motion or stretch-out redshift from the whole history of expansion during the light's travel time.
In fact one can do a complicated mathematical analysis involving a chain of overlapping patches---it's ridiculous but one can do it---so there might be a million observers between you and the object---and actually analyse cosmological redshift in terms of a million little Doppler shifts. But it is a clumsy and useless way to think about it.
I'm impressed. I haven't examined this closely enough to guarantee it but I think it should give approximately right answers if it is used over short enough distances that the rate r does not change significantly during the light's travel time.
When I quote this figure of 1/140 of a percent, what I mean is that this is the current
percentage rate of distance expansion. It has been larger in the past.
Vakkim, do you know the Hubble time? 1/H where H is the current value of the Hubble rate?
Have you ever calculated the Hubble time for yourself? I think you should, because you understand calculation, if you have not already.
What value of the Hubble rate do you like to use? I use 71 km/sec per Megaparsec.
Suppose I put this into google
"1/(71 km/s per megaparsec)"
What google gives me back is 13.772 billion years. I could round that off and say the Hubble time is 14 billion years.
Saying "1/140 of a percent per million years" is just a disguised form of this.
If the Hubble time (1/H) is 14 billion years, then the Hubble rate itself (H = 1/(1/H)) is 1/(14 billion years)
That is the same as 1/14 per billion years.
That is the same as 1/14000 per million years.
That is the same as 1/140 of one percent per million years.
In other words having calculated the Hubble time we could say the rate was "1/137.72 of a percent per million years", except that would be overly precise and we round off to two significant figures and say 1/140.
I expect this may be self-evident to you but want to make sure we know where the figure comes from, and that it gradually changes over time.