"A man who has a clock knows the time, a man who has two clocks is never sure"
Segal's Law
The two meters have a different response to the 23 KHz signal riding on the top of the DC so your DC measurements may therefore be different. I also suspect that the EEVBlog meter cannot measure a 23 KHz signal on AC which is why your AC measurements are so weird.
As for your changes in current drawn, the meters provide a capacitive load across a 23 KHz signal.
The correct reading is the one provided by the scope.