BlackBelt2025 "Basically, we need something that can read 4 analog inputs, do some relatively simple calculations, update some state, output 1 analog signal, and repeat. Ideally, we would like this entire process to run at 100kHz or more, but it absolutely must be faster the 80kHz."
"Is this possible on a Maple?"
The analogue input is okay. Maple's analogue to digital converters (ADC) can convert at up to 854k samples/second.
Updating modest amounts of state is okay.
Hard to say about the calculations, that depends on how much code is needed.
However, the Maple has no digital to analogue converter (DAC), so either use a different chip or add a DAC. If you are not a hardware person, then, use a microcontroller with built-in DACs. For example the Maple RET6 chip has dual DAC (if you can find a supplier), or you could try one of ST Micros STM32F3Discovery boards which have dual DAC (and are about $15).
"Our input and output ranges would be -2.5V to +2.5V"
That is a bit trickier. The input voltage range for ADC (and DAC) is 0V to 3.3V. Have you access to anyone who could help with electronics?
"I have read about the Dual Simultaneous Analog Reads, and I think that may be perfect. My only question is how this affects the accuracy and resolution (we need at least 12-bit) of the result."
I haven't noticed any warnings in the datasheet or manual to say that the specification degrades when using dual modes.
http://www.st.com/web/en/resource/technical/document/datasheet/CD00161566.pdf
http://www.st.com/web/en/resource/technical/document/reference_manual/CD00171190.pdf
The sampling rate is mostly determined by the 'impedance' of the input signals. If the input signals supply enough current the ADC sampling electronics can sample the signal quickly. If not, the sampling rate has to be reduced until the signal is adequately sampled.
Summary: standard Maple and Maple-mini have no output digital to analogue converter (DAC), so that needs to be solved. The +/-2.5V will need to be shifted and compressed to fit into Maple's 0-3.3V range (a common problem for most microcontrollers).
(full disclosure: I am not a member of LeafLabs staff.)