Admittedly, I've never used a meter to check PAR. I have read the lab report on the Illuminas, however. The criteria is the lamp hanging 6"/15cm over the water. This is important as part of the measured PAR is due to the reflection and refraction of the light that is achieved at this height. The Illumina does not use an optic to concentrate the light, rather utilizes the LED's lens to spread the light and this factor is calculated for. that is to say, if the light is hung higher on a typical tank, you will loose light from the wide angle of the lens. It never hits the water. A height over 6" is only recommended when the tank has a width over 24".
The actual lab test gives 260 PAR at 50cm below the water surface in a 60cm wide tank when the lamp is hung 15cm over the watet surface. (aquarists measurements are typically higher that the tests, as moving tank water can augment the PAR value). Light emmision is pure air will be different, as air has a different refraction index! Part of the genius in these units is their use of factors that are ignored by most designers. It's a bit like cooking; two eggs can be fried, scrambled or turned into an opulent omlet. It is technique that makes the difference, not the eggs.
Also, I should mention that your tank is plexiglass, which has a different refraction index than glass. There will be slight variations in PAR, although most of the reason you are not reading what you expect is the height of the lamp over the water surface.
As to PAR in itself, we should always remember that a PAR meter is registering all light waves in the photosynthetic spectrum as part of the PAR value. That means light that is actually not very usefull to corals will be registered as PAR, which makes this a questionable parameter. When the utilized LEDs are in the cool white to blue-violet spectrum, then the measured PAR will be of use. If the lamps are producing large amount of light in the yellow to red spectrum, also part of PAR, you will get a high AR value, but not of the radiation your corals require. Ultimately, one must run a unit for a few months to really be able to judge its effects on your coral community. Using the blues alone will give a low PAR value, however, this is the part of the PAR spectrum that is vital to the corals. It is simply difficult for a par meter to read properly, or better said, to put it in the proper context.
Does this help?