Six 30A circuits, eh?
And it requires neutral? Are you sure? There's no logical reason to need neutral, and if their cold cord is 10/3, remember this is cordage and in cordage, the /3 number includes ground. Regardless, it doesn't change what I'm about to say about conduit derate. In a split-phase circuit, neutral is not counted for wire count derate.
Here's how the math works with conduit derate (at least on the south side of the 49th parallel). You look at the wire capacity of the wire at its maximum temperature - 90 degrees C for THWN -2, THHN or NM -B. Multiply by 80% for 3-6 wires, 70% for 7-9 wires or 50% for 10-20 wires. And in split-phase supply, all circuits have 2 wires that count. So with 3 circuits, #10 wire is good for 32A, with 4 circuits 28A (which you can still get away with) and 5-10 circuits only 20A (no good at all).
So I recommend 2 conduits with 3 circuits per conduit.
Each conduit only needs 1 ground wire. You don't need to design for each circuit to have a ground fault at the same time!
That's either 7 or 10 wires depending on if you need neutral. Both are allowed in 3/4" conduit, but 10 wires in 3/4" is the statutory limit, and that means a very challenging pull.
However if you are very committed to 6 circuits in 1 conduit, you must derate 50%. You need 30A service, so you need wire capable of 60A at its highest operating temperature. For THWN-2, that's #6 copper or #4 aluminum, which allow 75A which you derate to 37.5A. Assuming 13 wires (12 conductors + 1 ground), you'll want 2" conduit for #6Cu or 2-1/2" conduit for #4Al, to keep the pulling effort "merely brutal" instead of totally impossible. If neutrals are required go up another 1/2".
Upside, with #4, remarking is now allowed, so you can buy all black and tape it white or green for neutral and ground. Downside, you need to provide large cavities for wire splices with consideration for bending radius.