You had me off on the wrong track with the term "bias",until read the rest of your posting.
"Bias" actually has a precise meaning when applied to amplifiers,so "difference" would be better.
1.5dB difference in power amounts to a power ratio of 1:1.425,so that if.say,the lower channel was 10 watts output,the other would be 14.25 watts.
If the "sound meter" is the sort of thing with a calibrated microphone on the front,used for sound pressure measurement,they are quite touchy as to positioning,so you may well have a discrepancy of that order.
Have you tried swapping the speakers to the other channel,to see if the sound level difference swaps sides?
As to looking at the outputs with an Oscilloscope,one thing you have to determine,is whether you can connect the earth clip of the 'scope to either of the speaker leads.
Back in the valve (vacuum tube) days, the speaker transformer effectively isolated the speaker voice coil connections from any DC power supplies,but in some solid state amplifiers it does not,so you may possibly damage something.
It would be wise to check this.
If there is a problem,you could still check each channel separately by using the two channels in the "differential mode".(check your manual).
If you use 10X probes,you shouldn't have anything to worry about as far as the voltage at various power levels is concerned.
By the way,if you are suspicious of the preamps,why not test them first?