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I did some extra testing to see about that.
The Cargoman did not improve the other district!
And I've also checked about the Canals and Orchard:
Strangely the Canals did decrease the value of the adjacent Village from 912 to 798.
Once I had upgraded the Canals to an Orchard, the value of the Village went back to 912.
But an Orchard does indeed increase the value of a craft district.
In my testing the increase was ~1.3 .
Also, the Orchard doubles the original value of a Commons, while the Cargoman multiplies it by 1.8.
To sum it up, the documentation and the in-game information is partially wrong.
And the arithmetic programming is even more mind-boggling.
But the game is easy enough to make this not much of an issue.
Also, in my testing, Takeda Shingen died consistently in May 1575, at the age of 55, after the second time he got sick.
I used Gifu castle for testing. The three districts were the number 2 and 3 right from the top for conscripts and the one right below them, which affects both, for agriculture.
The starting conditions were that the conscript districts, lets call them D1 and D2 (from left to right), were not developed so far.
District 1 had a starting value of 705 and district 2 of 690.
Here are my results:
No Cargoman:
Both converted to Drill Grounds: D1 705>987 and D2 690>966. Total gain = 558.
D1 to Drill Grounds and D2 to Garden: D1 705>1269 and D2 still 690. Total gain = 564.
With Cargoman:
Both Drill Grounds: D1 705>1128 and D2 690>1104. Total gain = 837.
D1 to Drill Grounds and D2 to Garden: D1 705>1410 and D2 690>828. Total gain = 843.
The Garden does multiply the value of the Drill Grounds by 1.8 at 1269 / 705.
And the Cargoman has a variable multiplier that gets lower with higher values -> ~1.14 at 1128 / 987 and ~1.1 at 1410 / 1269.
Furthermore, it shows that it doesn't make much of a difference if you combine a Drill Grounds with a Garden, if it's only two adjacent districts, but if you do, make the better district into a Drill Grounds.
If you are in a situation where the Garden can affect more than one district of conscripts, then it's worth definitely increases.
Personally, I try to plan out my bases in a way where multiple conscript districts are grouped together and a Garden can influence two or more, to get the most out of it.
Even more so, after I've done this testing. ^^