I think you're going to have a bad time getting consistent results. Any 2 good quality meters should measure the same exact voltage, but the disparity between the voltages on consumer grade PSUs is going to be crappy from the disparity in the components used in the factory to their age, even wire gauge and length will dramatically alter the power output as well as the draw from the PCB. Thats why your ATX PSU works on the NAOMI1 but not the NAOMI2 likely it's drawing more heavily and and the drop across the lines is enough that the voltage is out of range by the time it reaches the PCB. ATX PSU's are "self adjusting" but they don't know the voltages at the other end of the wire, plus PC hardware is designed to be really lax when it comes to this stuff but arcade hardware is not because it didn't have to be due to adjustable PSUs.
Instead why not buy something like the Meanwell QP-100-3A? it offers 3.3V 5V 12V and -5V, amperage output is inline with a JVS PSU and it hooks up like a classic arcade PSU plus it allows for adjustment on all the output voltages. Meanwell make PSU for industrial applications so it'd probably outlive original arcade PSUs anyway.
spec sheet:
http://www.meanwell.com/mw_search/QP-100/QP-100-spec.pdf
a place that sells them:
https://power.sager.com/qp-100-3a-2...M5QgxlZnD2KxdedMQxoCXkXw_wcB#dvSpecifications
There are cheaper adjustable industrial PSU options if you don't want to front the cash for a Meanwell.
Alternatively you could use an original arcade PSU and supplement it with a dedicated 3.3V supply. Sega did this on their official JAMMA kit for the Model 3 as well as in upgrade kits for machines moving from Model 2 to Model 3
Something like the Meanwell RS-50-3.3 again it's adjustable and it's only $16
spec sheet:
http://www.meanwell.com/mw_search/RS-50/RS-50-spec.pdf
a place that sells them:
http://www.mouser.com/ProductDetail...r28WdrYZgydYcvh9At9X6fCmJZIZZ_l0P9xoCDy7w_wcB
I plan on running a similar 24V model for use with gun recoil.
...just something to consider. Personally I try to avoid consumer grade parts for arcade applications whenever possible.