That's a heck of a trip, I think you have some larger considerations beyond boat choice here. The Carolina is an ample day tripper/overnighter and, you're right, might limit you a bit in packing. A bigger boat will give you more room and probably better speed/tracking but I would do two things before investing in a new boat:
1) Look at your maps. for a trip of this size you will absolutely need resupply points along the way. Not a big deal on the Mississippi. What's the maximum amount of time between resupply points you expect?
2) pack your current boat. Just see if it will all fit, and then take it out on the water and see how it handles. Before you can be certain what you want in a tripping boat you have to load it down and see how it handles. load it up with the gear you think you'll need between your furthest resupply points, then add 10%.
I've done a few long trips, one ~60 days, and in the end having the lightest most efficient best looking gear possible is luxury only. Good durable gear that you can afford is all that matters. A few years back I thought about doing the Missouri from source to sea (Mississippi for a big chunk) and ultimately decided not to do it. Mostly, for myself, I just didn't want to paddle the Mississippi for months on end. big slow flatwater through cities and farms wasn't my thing. But hey, maybe it's yours. A few things to consider:
1) there is likely to be little or no camping in long stretches of the river. Some farms will be fine to camp on, other farmers may fire at you with shotguns, who knows?
2) you have to carry all your water between resupply points. The river is not drinkable in any stretch of the imagination. Carrying lots of water is tough in a kayak.
3) Crime/vandalism. Around larger cities I know I'd not be comfortable camping conspicuously out in the open.
4) Barges. these can be hazardous to a kayak and won't be looking out for you.
Not trying to rain on your parade at all, just always better to consider problems than be surprised by them. Good luck!
if you did it this year you'd be making good time!
"Paddle silently, boof loudly"