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You confirm that works with the charger connected. Are you sure the battery is fully charged?
Unless the engine is tight or higher compression or hydro-locking and it needs the extra oomph of the charger I don't know what else you can do either.
your battery readings sound to be Ok when checked and the charging rate sounds Ok ... you need to do a load test to see if it is really good or just looks good ...
put your meter on the battery terminals and leave them on while trying to start the bike ... watch the meter as you press the starter button, if it drops below 9.6 your have a bad battery ...
If you have the meter connected and the voltage drops to around 10.5 volts when you turn the key on it would indicate a bad cell.
If it still reads 12.5 or so check when trying the starter. If it drops down to 9.5 volts you have lost too much of your cranking capacity and will need a new battery.
Each cell should be about 2.1 volts, 6 cells together gives you about 12.6 volts.
When you charge a battery with a bad cell, the other 5 will actually charge to a higher voltage (about 2.5 volts each) that is drained off almost as soon as any current is drawn.
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