Estimating the Weight of Tyrant's Pet Turtles

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: D&D.Sci: The Mad Tyrant's Pet Turtles, published by abstractapplic on March 30, 2024 on LessWrong.
This is a D&D.Sci scenario: a puzzle where players are given a dataset to analyze and an objective to pursue using information from that dataset.
You steel your nerves as the Mad Tyrant[1] peers at you from his throne. In theory, you have nothing to worry about: since the Ninety Degree Revolution last year, His Malevolence[2] has had his power sharply curtailed, and his bizarre and capricious behavior has shifted from homicidally vicious to merely annoying.
So while everyone agrees he's still getting the hang of this whole "Constitutional Despotism"[3] thing, and while he did drag you before him in irons when he heard a Data Scientist was traveling through his territory, you're still reasonably confident you'll be leaving with all your limbs attached (probably even to the same parts of your torso).
Your voice wavering only slightly, you politely inquire as to why you were summoned.
He tells you that he needs help with a scientific problem: he's recently acquired several pet turtles (by picking at random from a nearby magic swamp), and wants to know how heavy each of them is, without putting his Precious Beasts[4] to the trouble of weighing them. To encourage you to bring your best, he will be penalizing you 10gp for each pound you overestimate by
(An advisor with robes like noontime in summer rushes to the Tyrant's side and whispers something urgent in his ear before scuttling away.)
which will be deducted from the 2000gp stipend he will of course be awarding you for undertaking this task, because compelling unpaid labor from foreign nationals is no longer the done thing.
(The bright-robed advisor visibly sighs in relief.)
However, he snarls with a sudden ferocity, if you dare to insult his turtles by underestimating their weight, he will have you executed
(An advisor with robes like the space between stars rushes to the Tyrant's other side and whispers something urgent in his other ear before scuttling away.)
that is, he'll have you maimed
(The Tyrant looks briefly to the dark-robed advisor, who shakes their head sadly.)
lightly tortured
(Another sad head-shake.)
he'll deduct 80gp
(An encouraging gesture.)
for each pound you underestimate by
(An approving nod.)
and he'll also commission an unflattering portrait of you to hang in his throne room.
(The dark-robed advisor gives the Tyrant a big smile and two thumbs up.)
The meeting apparently having been concluded to his satisfaction, the guards see you out. Some time, some help, some adverse reactions to ambient magic[5], and several waterlogged sets of clothes later, you have a dataset representing a random sample[6] of the other turtles in that swamp. You also convince some palace officials to give reliable testimony on some characteristics of the Tyrant's pets, though no-one is willing to provide any actual measurements[7].
What numbers will you give the Tyrant?
I'll post an interactive you can use to test your choices, along with an explanation of how I generated the dataset, sometime on Monday 8th April. I'm giving you nine days, but the task shouldn't take more than an evening or two; use Excel, R, Python, Tiger Instincts, or whatever other tools you think are appropriate. Let me know in the comments if you have any questions about the scenario.
If you want to investigate collaboratively and/or call your choices in advance, feel free to do so in the comments; however, please use spoiler blocks or rot13 when sharing inferences/strategies/decisions, so people intending to fly solo can look for clarifications without being spoiled.
Notes:
You may assume that you are wealthy and courageous enough to prioritize maximizing Expected Value, though the value you assign to providing honest estimates and to the possibility of...