0.08 volts, 80 millivolts. That's the sort of reading I was expecting. There are some caveats about its accuracy but the main one (measurement lead resistance) has been dealt with already when you showed the resistance reading. The other important one is that the meter will be reading only the voltage present at frequencies within its measurement capability, which includes all electrical power lines. However if you were under the mast of a radio or TV station transmitter, that might not be a sufficient indication that there were not strong fields at radio frequencies inducing a voltage that the multimeter cannot sense.
I think you need to look carefully at what other factors could be influencing your sensation of the effects of the mat; they can be real effects, and again I must say I am not doubting what you experience. But 80mV w.r.t. true earth, contacting the body in at one point only and relying on the stray capacitance to earth to complete the circuit, cannot realistically pass enough current to create a sensory effect.
The stray capacitance of a body is typically less than 1nF, more likely around 200pF. It will be less to true earth if part of your environment is shielded from earth by the mat at mains earth. Let's call it 500pF anyway.
At 50Hz, 500pF will have a capacitive reactance of 1/(2*PI*50*5e-10) ~6MΩ
0.08V between mat and true earth gives a touch current between you and the mat of 0.08/6M = 13 nanoamps. I can just about feel a current of 10,000 times that, when concentrated in my finger and I brush it over a surface to maximise the sensory response to muscular reaction (like a dowsing rod). It takes about 100,000 times that current to feel as an actual electrical tingle.
You'll probably still think I'm crazy after watching this, but it could be really eye opening for you too
I will watch the whole thing. I have just watched the first two minutes and counted six factual errors or abstract ideas presented as facts.