Using a DAC I think I'd need a lot bigger resolution DAC, to compensate for the "lost resolution" after 1.25V, which is the max adjustment voltage for the CC chip I mentioned.
This isn't an issue at all. You can scale the output of the DAC as needed, either externally, or by selecting a more appropriate reference voltage. Or if you're mixing a DAC into a driver's feedback node, you compensate for this naturally in the design of the summing network.
I did think of using feedback from the LED current to verify stability, but not to improve stability. I'll give that a go.
Careful with this. Improving performance by adding an extra current feedback loop -- which is essentially what you're talking about here, a slow current control loop that corrects the fast current control loop in the driver -- requires that the outer loop be substantially better than the inner loop in the ways that you care about. Using a single outer loop with a single ADC/reference is great for improving consistency across the three drivers, but at the same time it subordinates the accuracy/stability of the drivers to the accuracy/stability of the outer loop. If the new outer loop has, for example, a voltage reference with substantially worse drift than the voltage references in the drivers, then you've just made the drift of the whole system worse by adding that outer loop.
To do this right you should start with a high quality voltage reference and measurement ADC. Those are the most important factors in this, and should be picked for their specific performance characteristics, rather than just whatever's built into an MCU. The DACs are less important, as long as they provide sufficient resolution, since they are inside the loop. The exact MCU doesn't matter at all, it just has to read from the ADC, do some math, and write to the DACs -- anything will do that. Fundamentals are important too, of course, all of the normal rules for precision mixed signal circuitry apply. Phasing of the measurement against ripple also matters.