Just to be sure, is the state of charge of the batteries low enough to accept a higher current
How are you measuring the charging current
If the alternator
is delivering more current when more demanded, it seems to be a problem in the path or perhaps the battery
How old are the batteries? Has this deteriorated over time, or suddenly changed?
Check for bad connections in the path from the alternator to the batteries. You can use a multimeter to measure the voltage drop across the positive path then the negative path with the engine
on. It should be less that 0.5V. Higher than that indicates some resistance in the path. With the engine
off the same paths should show near 0 Ohms resistance.
I've found Charlie Wing's book pretty good for explaining and helping think through troubleshooting process.