How can I install Snow Leopard on a new iMac or install FCP6 on Lion?
The problem is that new iMacs probably don't support Snow Leopard. Perhaps upgrading a Snow Leopard installation with all the apps you need already on it could work.

Well, I see 1 possibility: install Snow Leopard on an external HD (using a computer that supports Snow Leopard) with all the latest Apple updates, then install FCP. Once that's done, use Disk Utility or Carbon Copy Cloner to clone this external HD onto your iMac, then see first if it's starts and behaves correctly, then try the upgrade to Lion.

This is the jist of it, but if you need more instructions, let me know.