As far as I know, that won't work. If I'm understanding you right, you basically want RAID 1+0 but across two seperate enclosures?
The problem here is, the two enclosures. In order to do RAID 1+0 you need to have all the drives on the same controller, or at least one two controllers designed to talk to each other.
I would suggest doing your RAID 0 setup as you planned, and using backup software to backup the first array (which will appear as one drive) to the second array. Also, I don't think you are going to get 8GB. I think that Lacie 2Big is two 2TB drives is it not? Hitachi is the only company I'm aware of making a 4TB drive and I don't even know if they are shipping yet. Either way, they are $400 a pop, I doubt that's what the 2Big is running. In RAID 0 mode it'll be 4TB, in JBOD mode it'll be 2x2TB, and in RAID 1 it'll be 2TB. That is, unless you meant you want to combine all 4 drives into an 8GB RAID 0, in which case no, you can't do that on two separate controllers. I wouldn't advise it anyway, if you lose one drive you lose ALL of your data. There is a 5% annual fail rate on hard drives, 4 drives each with a 5% chance of failing in their first year (that fail rate increases each year), those are not good odds if your data is important.