2xAAA battery => 3.3v/250mA step-up converter with logic-driven power control [superseded]
Size constraints: The challenge would be the 4-5mm height, rather than the other two dimensions: A boost converter will typically require an inductor, likely to be the tallest part.

For instance, this prebuilt 1 V --> 3.3 V boost converter module is 12x22mm, but the inductor on it is 6 mm tall:



This example does not offer an enable pin, though - My cursory search shows several 5 Volt and 12 Volt boost converter modules with an enable pin, but not for 3.3 Volt output.
EMI constraints: This is a tougher problem. A typical boost converter works by switching currents on and off using an oscillator, hence even with the filter capacitors on the board, there will be some EMI at the oscillation frequency and its harmonics. These modules certainly are not medical-grade electronics. "Virtually zero" is virtually impossible. 

An option is to use a 5 Volt boost converter like this one, followed by a low drop-out, low-ripple linear regulator to produce the desired 3.3 Volts. The 3.3 Volt rail then will have negligible noise. 



Direct EMI radiation, especially from the boost converter's inductor, will still be an issue. To address this, shielding the entire assembly with a metal box or mesh would help. Only your own testing will reveal whether this serves the purpose sufficiently.
Microcontrollers typically work perfectly fine even with fairly noisy (50 to 100 mV ripple) power rails from boost converters. Also, a hybrid incorporating an LDO, as suggested above, addresses this issue completely. 
The "enable" pin in the 5 Volt boost converter suggested above could be toggled by the DTR pin - but then how would you be supplying power to the serial device when the boost is off? 

For similar applications, I have used an unregulated supply (just capacitors) from the AAA cells into a minimal microcontroller such as the ATtiny85, and used the microcontroller's output pins to toggle the boost controller supplying the rest of my device. Consider whether this works for your design.