Sorry to the OP and your goodself. I was in so much of a rush to help, I completely forgot 'Lighting 101'!
Yes, my monitor is 350 cd/m^2 max and 38% of that is 133 cd/m^2. Good estimate on your part.
The sad part is that I knew most of the the above apart from the paper details. I'm old . . what I knew a few weeks ago, when testing ISO on some of my cameras, today has gone away.
Thanks for the correction!
Ted
Ted, no problem. But getting back to the OP's issue of a very large difference between his cd/m^2 here's what I do with a good lux meter.
1. Get a good unprinted matte paper. Assume WP L* is around 95 to 97
2. Position it from a lamp so that the Lux level at the surface is approx. 1.1*3.14 the monitor's presumed cd/m^2
3. Now the monitor's white should be the same luminance as the paper from the lamp. If not, adjust the lamp distance so that they match.
4 Then read the Lux level at the paper's surface and reverse the calculations. For instance if the Lux level is 350 then the monitor's Luminance, when matching, would be about LuxReading/(3.14*1.1) or around 110 cd/m^2