DaveSt, your camera should have 3 whole stops of headroom above "middle grey" before you start to see clipping. What you have done is to meter the white paper as though it was a grey card (the camera has no idea whether it is white, grey or black, but it sets an exposure to render the paper as though it was middle grey) and then increase the exposure, rather modestly, to put the paper at +1. That is not enough. If the white paper is only at +1, what sort of things can you think of that would be brighter than sunlit white paper? Apart from light sources or direct reflections of the sun I can't really think of anything that would make use of the further 2 stops you have to spare. Maybe some paint and plastics could be a little brighter, but I doubt by 2 stops. In my opinion you should be placing the paper at +2 stops (at least). That will still give you a whole stop to spare and, if you shoot raw, even more headroom that you should be able to recover, if you clip one or more channels.
Also, I'm not sure about how you are metering in the first place. IMO you should use a metering mode other than Evaluative and you should fill the metered area with the subject. If you use CWA metering then you need to fill the whole frame.
Once you have sorted out a "correct" manual exposure for the paper, then you can meter off your palm and see what the reading is.
An alternative approach is simply to pick a bright sunny day and set an exposure that matches the "Sunny 16 Rule", such as f/16, 100 ISO, 1/100. Then face away from the sun, hold up your palm in front of the camera, making sure not to cast a shadow on your palm with the lens, and then note the meter reading. That should be what you aim for. I recommend spot or partial metering in order to ensure you are only metering your palm and not the surrounding scene.
Lastly, I have white skin and metering my palm at +1 1/3 works well for me. If you have dark skin then (in my limited experience) you may find that something like +2/3 is better for you. It's also worth noting that such an exposure should preserve highlight detail in brilliant white things, such as a sunlit swan's feathers, but if your scene contains nothing very bright/white then you may do well to increase the exposure by 1 stop in order to capture more shadow detail. An example would be a brown or black dog against a background of grass.