If you need 5 volt digital compatibility, the Teensy 3.2 might be the best compromise, which is poor word to use since the 3.2 can run circles around any AVR without breaking a sweat.
An Arduino DUE fits all your requirements, except the EEPROM. Although you can store variables to restore after power down with the DueFlashStorage Library (stores in the 512 KB of Flash).
Direct register programming for ADC conversion (12_bit ADC) is definitely the best option. Several example sketches can be found in the DUE sub forum of the Arduino forum. This board has 5 Serials plus one SerialUSB.
You can buy the brand new version of the Arduino DUE from arduino.cc:
ok,
At a first glance the weight is on teensy. On the other hand, perhaps the more digital outputs and the DACs go on favor of DUE (future use, other projects-same platform).
I believe I have to read some things about .