If you end up deciding to out source the whole thing, I inquired to broke studio in france who do everything (cart, manuals and boxes) and also put the product on their website with their other decent titles. This probably wont work out the best financially but could save a heap of time.
I use Instant print a lot for my lego display business but they don't tend to be interested in anything custom. I enquired about some arcade machine decals and using my own cutting paths once and they didn't want to know.
I've also used BestPrinting UK who do things like spot UV which could add some 'pop' to your boxes and they're super cheap! My missis just started using a new supplier for her candle labels but I'll have to ask her about those tomorrow. I'll test one out and see if they might be good for cart labels.
I'm sure you know what you're doing but when I first started outsourcing printing I just used the cheapest on ebay and you get what you pay for! Ideally you want solvent based printing or UV cured not waterbased inks. I'd be more inclined to pick a bigger online printer than a local outfit as I think you're more likely to get consistent quiality done on the same machines with the same ink profiles etc. Thats just my paranoia though lol.
Regards cutting and folding, this is something you're going to be doing a lot of. My best advice is to invest in a hobby electronic cutting machine like a Cricut or Silhouette. If you checkout John Riggs on Youtube hes got a video about making NES labels using the machine. We have a Cricut which I use to cut and fold light weight boxes. If you're any good on illustrator or vector programs you can design the cut path on that and import it. Thought I'd mention this incase you weren't considering it. The NES box should fit on the larger mats they use. If you need any help of advice on this you can PM me. I've used ours for all sorts of projects.
I have a different opinion to slobu. I don't think the printing should be done on home equipment. As a customer I'd be pretty pissed to pay £40 - £50 for a boxed game that looked cheaply done. Also would'nt use universal jewel type cases for the same reason. Each to their own and I'm not saying anyone is wrong, its just my preference. I'd do an old school card NES box but modernise is a little maybe with the Flea logo in spot gloss or something.
I hope this helps a bit.