Although the pi has been enormously successful in terms of volume - the Foundation originally planned on about 10k units, so somewhere around that volume you probably could design your own.
The processor on the pi was cost optimised and isn't really that great, but it does have a nifty GPU built in that you don't seem to care about (so why pay for that?).
I don't think you'll be able to get the CPU/data sheets from Broadcom for just 10k units. The Foundation has some members that work for Broadcom and managed to get a great deal on the processors.
Part of the attraction of the pi is that apart from a couple of minor variations - everyone is running the exact same hardware so it's easier for people who aren't experts to get help from people who are.
So you want an ARM CPU with a bunch of RAM - some GPIO and 3G (probably via USB)? If your volumes are high enough you can probably make something around the same price of the pi, but the pi would be a crappy starting point.
I'd have a look at the open source Beagle Bone Black instead