dc42:
I'm late to this thread; but did you consider the ATSAM4S processor range? They are a fraction of the price of the ATSAM3X8E processor used on the Arduino Due, but faster and with more RAM and a Cortex M4 core. From a programming perspective, they are very similar to the ATSAM3X8E, so firmware for the Due would be easy to port.
hiya dc42, nice to hear from you on here. ATSAM4S8CA-AUR Microchip Technology | Integrated Circuits (ICs) | DigiKey so something like that one, which is a 100-pin LQFP, and $2.89 in reasonable volume.
checking on taobao... yyyehh they look like fakes which probably means the only way to get it would be to import it. atmel's presence here in shenzhen just... doesn't seem to be as good, except for the 8/16-bit stuff.
also: the due reference design is actually for a 144-pin ATSAM3, and the ATSAM4S series doesn't have a 144-pin variant. they really really struggled to get a good pin-compatibility on the Due, with the 144-pin ATSAM3.
the ST 32-bit processors on the other hand, some of them seem to be extremely common, and easily accessible. i've been able to get hold of the STM32F427VIT6 here for example, and will try th STM32F401VET6 next. or.. i would... if it had DAC 
i will keep searching.
so you know i'm doing this primarily for a 3D-printing board, if i was doing an SBC then yes i would definitely look at the ATSAM4S. i'm... experimenting, here as i do, i want to see what's possible.