RollCycling...I think you may be confusing Gross Tonnage with...

RollCycling...
I think you may be confusing Gross Tonnage with Summer DWT (Deadweight).

eg Generally speaking:
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For ships, the gross tonnage is not weight. It's volume. Specifically, it's the size of all the moulded spaces.
(A vessel tonne = 100 cubic feet, or 2.83 cubic metres).

As you can imagine, a full load of styrofoam may take as much room as a full load of Iron Ore from Riley, but they'll weigh differently.

So the Gross tonnage (GT) is used to calculate port dues, safety rules, registration fees etc.

Meanwhile the DWT is the weight that a ship can carry, but not just cargo. It also includes fuel, crew, their food, clothes, and whatever snow globe collections they may have from every port they've visited.... you know, assuming they like snow globes, LOL.

The temperature and salt content in the water also changes how much weight a ship can carry from season to season.

That's why the outside of each cargo hull is marked with depth codes...
Kinda like "fill up to here", if you're sailing in:

TF – tropical fresh water
F – fresh water
T – tropical seawater
S – summer temperate seawater
W – winter temperate seawater
WNA – winter North Atlantic
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Specifically in this case for the Diamond Queen, we don't need any paid-for service.
The public data is sufficient:

Gross tonnage (volume) = 34,800

So volume in land-lubber speak = 34,800x2.84 = 98,484 cubic meters.

Assuming the DSO Hematite from Riley (Direct Shipping Ore) weighs 1.81 to 2.45 t per cubic meter, (depending on moisture content, Fe grade etc by wikki standard weights for IO), then it follows:

46,000 tonnes of Iron Ore from Riley only needs 18,775 to 25414 cubic metres aboard the ship.

Also; Summer DWT = 61,414.

The actual cargo tonnage is DWT minus tonnage for passengers, crew, fuel, ballast, food, and ship supplies... which I can guestimate too, but we hardly need to. It's not summer yet, so there's a healthy safety margin just there.

& No matter which way we look at it, the Diamond Queen is plenty big enough for our first shipment.

Nice name for a vessel too actually. Wish I could be there to welcome her in.
At the moment, she's off the coast from Woolongong, headed for Port Kembla first.

May she and all her crew arrive and depart again safely.