10A is nothing; the alternator, depending on model, can output 120-140A, with the battery as the buffer. With the key in the on position, the car can draw 60A. A good coding-capable charger will be able to demonstrate that; maintaining 13.8V to the car while reading codes and testing modules I have seen the charger jump to 63A (capable of 70A). I agree that a dead battery shouldn't be charged in the car, but just as the battery is designed to absorb excess alternator output, it should absorb excess charger input (unless the charger is crap).
Hope you get the cluster back! Have you tried the gremlin removal process (disconnect battery)?
'99 528i ('98/12 build). 282,000km BY29428/Royalrot
Breaking My Wallet since 2009
Mods: Stoptech SS brake hose, 280piece toolkit resting on trunk floor, Beisan VANOS seals, increasing amounts of duct tape and glue
'99 540i (grandfather's)