I got the C6 cross member from autokrafters, but it is a very different style. My old cross member is a rectangular style shown below and my new one looks more triangular also shown below. As for headers, I am running 2v heads, with a valve job and porting.
Yeah, you'll need a driveshaft cut to length and balanced.
But, the C6 shouldn't have any issues with clearances in the 67/68 unibody.
However, mock it up and install it just to be sure. You can do this relatively easily with an empty C6 case. Get a junker, pull the front pump and valve body, then shake the guts out of it and *voila!* lightweight mock up trans case. Bolts to the bellhousing and your mount, lets you see what's up before you get the real one in there, and is easier to wrestle around even if you're using a lift. Costs maybe 25 bucks for a cracked case core or a junkyard part is a bit more, but not much. Not much demand for the c6 nowadays in the used parts biz.
Hey buddy I know this is an old post but I've installed the 351C with a C-6 in my 67 and it fits great. Compared to the 289 I feel its easier to access the headers and spark plugs. Used factory motor mounts and C-6 crossmember and it all bolted right in. Hope yours is a success too