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If there is a problem at low power usage then you can easily solve it by temporary add more power. Lets say add a 40watt lamp or something, later remove it from the calculation.
While it sounds a bit hacky, I think this is an underrated solution. It's actually quite a clever way to bypass the whole problem. Physics is your enemy here, not economics.
This is kind of like trying to find an electric motor with the highest efficiency and torque at 1 RPM. While it's not theoretically impossible, it's not just a matter of price or design, it's a matter of asking the equipment to do something it's simply not good at, while you want to do it really well. It can't, certainly not affordably or without significant compromises in other areas. In the case of a motor, you'd be better off letting the motor spin at its much higher optimal RPM and gear it down, even though there will be a little loss in the geartrain it's still a much better solution overall and that's why essentially every low speed motor is designed this way.
In the case of an ammeter, it seems totally reasonable to bring it up to a more ideal operating range by adding a constant artificial load. In fact the high precision/low range multimeters and oscilloscopes are usually internally doing almost exactly the same thing with their probes, just in a somewhat more complex way behind the scenes.
Good point!