You may want to just simplify things, and run +12V directly to the Arduino's power jack.

This project uses very little current; it is a low power setup. I have it running on the test bench here, and the 12V current draw is only about 160 milli-amps (0.160 amps). Multiply that by the voltage (12V) to calculate wattage, giving about 1.9 watts total. The Arduino's onboard 5V regulator is hovering at about 28C (82F), with room temperature at 22C.

Compare this with inserting an extra, 95% efficient, DC-to-DC converter, to drop the 12V down to 7V, for input to the Arduino's 5V regulator. This would have a 5V drop (12V to 7V), and assuming the same current flow it would save (5V * 0.156amps * 95%-efficiency) about .75watts. So the setup would still be using about 1.2 watts, compared with 1.9watts without it.

The 0.75 watt savings are probably not worth the hassle/expense in this case, given that the circuit draws so little power. An extra 0.75 of a watt in heat is negligible here.

So I would just ditch the DC-to-DC converter altogether, and feed 12V directly to the Arduino, and use 3.3V from the Arduino to power the Betz board.

EDIT: If you were to forgo the USB connection, you could power the Arduino from a 5V DC-to-DC conversion. In this case, the converter would be dropping from 12V to 5V, a 7V differential, saving us (7V * 0.156amps * 95%) a whole watt. So power consumption would drop from 1.9-watts to 1-watt. That might be enough of a saving to consider the extra DC-to-DC conversion, but I still would not bother.

If the circuit used a lot more power, say in the 3-watt+ range, then yeah. But at 1.9W ? WTF cares?