Before you go this route, think about how high this door will be from the floor when opened; it may be unusable by shorter members of the household.

The manufacturer's price probably has more to do with the fact that you're requesting something odd from people who are set up to produce the totally predictable. Custom requests from any high-production facility tend to get absurdly expensive. Their price no doubt makes sense for their business model, but that doesn't mean it makes sense for you.

Appropriate hinge / hardware varies a lot, from $200 for fancier hardware systems. There's nothing magical about this hardware; if you have basic tools and woodworking competency, you can install them yourselves. You'll want to get your hands on the installation instructions for the particular hinges you'll use before ordering your cabinets, so you can make sure the cabinet parts will relate properly; the doors can only overlap the face frame / cabinet front by so much. If your cabinets will have concealed hinges then you'll also want to specify that the door for this cabinet doesn't get mounted or bored for the cup hinges.

Thanks jon - The cabinet I am planning to do this with is just over the sink, and only 12 inches high, so it should be easily accessible. I have found some hinges online that I think will work, and I plan to see what IKEA uses on their cabinets of this type before I decide. My DH is very handy and should be able to install them. Good point about asking not to have any door hingles installed by the manfacturer.

I may only have a vague idea of what you are trying to do, but another option may be to stay with the mfr. hinges so that they match from the outside and apply toy box supports.

Around my house we all range from 5'10" to 6'5" so reaching stuff at ceiling level has never been a problem.

Here is a link that might be useful: toy box lid supports

Blum hardware

http://www.blum.com/us/en/01/20/index.php

Hafele hardware

http://www.hafele.com/us/products/Lift-systems-for-wall-cabinets.asp