What’s the most efficient method of transferring gold between characters

According to this wiki, all pets are equal.

However, different fish produce different properties when fed to your pet.

I really wanted to disprove your statement as it was hard for me to accept that a human could be doing things faster than how it was implemented in the game, however, you're right.

To test this, I did something relatively easy. I've gotten myself a level 1 Outlander, dualwielded the pistols you start with (they fire every 0.88 second) and went to the dummy of Act I (with my pet on passive).

Since Outlanders get charge and this charge gives them higher Attack Speed, I used the console to always have full charge. This gives us a 10% higher attack speed and our guns should thus fire every 0.968 second.

Then I did 2 tests.
One where I did a 30 second combat parse with just holding the mouse to attack and one where I did a 30 second combat parse using an autoclicker to click every 10ms.

With the console command combatlog this parse gets written to a file. I removed unimportant lines from the file such as Player interrupted Dummy and was left with only lines that have attacks on them (either normal attacks or fumbled attacks, I tested till I had a series with no Execution attacks).

When holding the mouse to attack, there were 58 attacks in 30 seconds. This means an attack every 0.967 second (= trunc(58 / (2 * 30))). We see that this is indeed corresponding with the ingame displayed weaponspeed (see previous ingame weaponspeed above).

Now, when using the autoclicker, there are 62 attacks in 30 seconds! So we can achieve more attacks if we click ourselves (although really, really fast).

So your statement is most definitely true.
However, clicking once every 10ms like the autoclicker is somewhat hard to achieve.
I tested my own fastest clicking speed on this site and I got a result of 7 clicks per second or about a click every 143ms. Running the autoclicker with an interval of 143ms (he is more consistent than I am!) I get a total of 53 attacks in 30 seconds.

So even if it's technically possible to perform better by just clicking the mouse, I really doubt any of us can truly achieve the same amount of attacks as when just holding the mouse.