Ok so you know the circuit works, step 1.
Looks like noise is an issue, most likely conducted into the circuit via the supply, if the noise were magnetic it'd be there with a battery supply.
If your measuring current draw from a smps then you might have some rf noise issues, rf can produce large voltages between the pri and sec of a transformer, a lot of smps's have a cap that goes from the dc bus on the primary to the output for this reason.
Looks like noise is an issue, most likely conducted into the circuit via the supply, if the noise were magnetic it'd be there with a battery supply.
If your measuring current draw from a smps then you might have some rf noise issues, rf can produce large voltages between the pri and sec of a transformer, a lot of smps's have a cap that goes from the dc bus on the primary to the output for this reason.