You will have to go to the book and make sure your gutter is big enough.
My thinking, however, is why not come out with 3 - 2" conduits and run them over the 10' distance you are going and into whatever you are installing there (Discon's or whatever)?
You can't put all those conductors in one 3" conduit without derating them! The max length you can go without derating is 24"'s.
You need three seperate conduits. Big pipe is for big wire, not for many conductors.
Anytime you have more than 3 current carrying conductors in a raceway you have to derate them. See Chapter 3 in the NEC right before Table 310-16. There are notes there and a table showing you what %'s you would have to derate. And, you would have to go to chapter nine to see if you can even fit that many 3/0's in a 3" (never mind derating).
Unless I'm misunderstanding you, I would come out of the meter and hit my mains right there with seperate conduits. You can derate your neutral (by Code) but in practice you are probably better off not derating it.
Also, you need your MAIN(s) to be right there at the meter. You can't run your feeders unprotected (unfused) any distance at all except a back to back service for example. If you can't accomplish this you'll have to buy a MAIN for the service and then branch out.
A 6x6 sounds too small to me for all those conductors... You're going to have to do the calculations and make sure.