Digital force gauge query

Why is the reading on my brand new just calibrated digital force gauge different depending on whether I take the reading with my Mystic Mat on or off?
I wouldn't worry about it. Mine is the same way and the variance with mat on/ mat off is pretty consistent with two different turntables. Depending on the thickness of your mat, I would expect your readings are about .10 gram different. It may be anal, but I end up averaging the two readings to get where I want. Of course, there are those who say you should adjust by ear to finalize VTF anyway.

I actually think the mat off reading is probably more accurate for most records, unless most of your records are 180 or 200 gram pressings. Typically, the weighing platform, even on the best of the scales (I use the Canrong scale, also marketed for megabucks more as the Acoustech or Origin Live) is thicker than even a 200 gram pressing, giving you a slightly inaccurate reading compared to what a typical record is going to give you in terms of VTF.

Go for the average and don't sweat it.
I think your advise is spot on. I measured with the mat off as a means to compensate for the thickness of the gauge's measuring platform. I am using the exact same gauge as you, i.e. the Carong. My question is why, scientifically, even logically, should the readings differ merely because the plane of the arm is at a slightly different angle?
Leverage. As the arm is raised the weight shifts toward the counterweight slightly.
Just imagine an arm at a 45 degree angle (a very thick mat!) and you can easily see how the measurement would be lower.
1. The entire mass of a tonearm/cartridge is supported at two points, the bearing and the stylus.

2. Downforce (aka, VTF) is an measure of how much force gravity is exerting on the *portion* of the tonearm/cartridge mass that's being supported by the stylus. (The remainder of the tonearm/cartridge mass is still being supported by the bearing.)

3. When you raise/lower your scale (or arm base, as with VTA adjustment) it changes the angle of the arm. This shifts a small percentage of the armtube and it's mass from one side of the bearing support point to the other.

4. More mass on the scale side of the bearing = more weight being supported by the stylus = higher VTF. Less mass on the scale side of the bearing = less weight being supported by the stylus = lower VTF.
I measured my Mystic Mat against the platform of the gauge with a ruler and found them to be essentially the same height. So, to my way of thinking, these eseentially cancel each other out, i.e. placing the gauge directly on the platter is the equivalent of where the stylus would otherwise meet the mat. In order to allow for the height of a record, I removed the mat, placed an average weight record directly on the platter and placed the gauge on the record, measuring for the optimum VTF for my cartridge, which is 1.8g. Seems a logical solution.
"Just imagine an arm at a 45 degree angle (a very thick mat!) and you can easily see how the measurement would be lower"
Your example would cause an increase in VTF, not a lower value.