Uplinker, the Airbus and the NG are FADEC equipped. The aircraft types in question here use mechanical fuel metering and throttle cables and I suggest that arrangement could likely be the source of the oddity.
Lancelot:
When TOGA is selected, you should see the throttles move smartly in unison to a coarse "predicted" position. Once there, N1 feedback takes over, and the movement will be slower. The former (coarse) movement is dependent on position feedback from the mechanical fuel control in the engine and if rigged within spec, L/R levers should be fairly close to one another.
Cable rigging through the servo mechanism has been known to be a potential cause of stagger on the classic, but this is a sledgehammer approach that likely has already been eliminated by your mechs.
I may be out of date in my knowledge in the classic, but I thought the A/T system would be disabled on aircraft with intermixed engines.
Right engine lags behind left, for a few seconds, and up to 20% N1 difference.
On both aircraft? By a few seconds, I am guessing less than 3 or 4?
The thrust levers begin to advance as normal, but at about 75/80% N1, one thrust lever momentarily physically halts or even retards a fraction, requiring manual intervention.
Are both engines close in N1 when this occurs?