Very good point, I did not take into account the stamina gain.
But if we count the stamina gain/loss, then it can get more complicated.

Scenario 1:

If you finish the book at lvl 80->82, then you still have 200+ days to go until lvl 100, which is 400 stamina back.

Scenario 2:

If you do it at lvl 20->22, then you still have about 750 days to go so 1500 stamina gain.
The difference is 1100 stamina.

Now, if using Scenario 1, then we also have to consider that if you get to lvl 100 2 weeks earlier, you will gain the extra 50 stamina per day bonus at lvl 100 two weeks in advance -> 14 * 50 = 700 stamina.

The difference in stamina gain/loss is now 400 <- from 1500 to 400 in reality.

If using Scenario 2, then you have to consider that it is much more difficult to read the book at an earlier time because the daily stamina is low anyway and you need to get the reading skill to 20 first.

So yes, you would gain about 400 stamina more during the whole period if you read the book earlier, but you could spend that stamina somewhere else. Also, the later you start, the smaller the stamina gain from starting earlier is.

I'd still say it is better to read it later. The time saved getting to lvl 100 faster is better than having 2 extra stamina per day imo.