It's likely that the meter itself will not suffer from reciprocity failure. It will likely be quite linear over its specified range. Based on my experience, carbon is a fairly linear process (minimal toe/shoulder), so reciprocity failure should be minimal there, as well, unless you're using very high concentrations of dichromate. The combined heat and high dichromate concentration could cause fog very quickly, which I guess, is sort-of the opposite of reciprocity failure. Check either Sandy King's carbon book or his article in unblinkingeye, there are some graphs in there. Don't know much about other processes (Pt/Pd, cyano, etc.) in this regard.

If the meter gives a reading in mW/cm2 (linear units, not log), a one-stop difference is a doubling of the reading. e.g. from 5 to 10 is one stop, from 10 to 20 is one stop, from 20 to 40 is one stop, etc. Best thing to do is measure your UV-lamp output with the meter and them compare your sunlight readings.

# of stops difference between 2 readings = log( R1 / R2) / log(2)

For example: R1 = UV lamp reading, R2 = Sunlight reading. Positive numbers means the UV lamp is brighter (so you need to add that many stops to your sunlight exposure). Negative numbers means the sun is brighter, so you need to subtract that many stops from your sun exposure.

NuArc integrators just measure the UV output and slow down or speed up the counter. It does not give a calibrated measurement. One thing you'll need to make sure of is that the UV reading from your meter stays constant over the course of the exposure, which might be 30 mins. or more on less-than-ideal days. You might need to adjust your time if the UV goes up or down due to clouds or whatever.

Doing some back-of-the-envelope math on my Nuarc:
1000W bulb
1% luminous efficiency (pessimistic? optimistic?)
17x22 inch imaging area (assuming uniform illumination) = 24128 cm^2
10W / 24128 cm^2 = 0.4 mW/cm^2

One more thing...I took a look at the specs on the mfr's webpage, and the meter is fairly sensitive down to ~280nm. When taking a reading make sure to place a piece of glass over the sensor that's identical (or at least similar to) the glass in your contact printing frame. Ordinary window glass starts to absorb significantly around 325nm, so you'd want to exclude any energy that might give an erroneous reading, and to tune the meters' response to be a bit closer to what the exposed paper (or carbon tissue) sees, since it's "seeing" the sun through the glass. If you want to get fancy, you can get narrow band-pass filters that mimic the sensitivity of the alt-process you're using.