Sekonic L-358 exposure reading

I have recently purchased Sekonic L-358 light meter. Although it is quite convenient to get the better exposures, somehow the exposures looked a little to the bright side. I take a lot of painting pictures. So getting the right exposure and the color balance is very important.

The Sekonic L-358 manual says that when taking shots of paintings and flat copies, I need to put the lumisphere in lowered position. I bought an 18% grey card and tested the exposure readings of the Light meter and my camera (Canon 5D Mark II). The light meter reads the same exposure setting as the camera when the lumisphere of the light meter is raised. But when the lumisphere is lowered (which is instructed by the manual for flat copies), the exposure reading is 1/3 stop darker given the same lighting. In other words, the light meter is reading the same as camera reading when the lumisphere is raised. But according to the instruction manual I must use the lowered lumisphere for the flat copies and paintings.

Why I want to use the light meter instead of the grey card is because I am using Strobe Flashes to light up the paintings. And with the strobes it is impossible to use the grey card exposure test in advance.

I hope my writing makes sense. My question is: When taking photos of paintings, do I use the lumisphere raised position which reads the same as my camera exposure reading, or to use the lowered lumisphere according to the instruction manual which is a little bit off balance than my grey card and camera reading? What are the other solutions?
Thanks.