Speaking of the LT3081: I wonder if the current monitoring output is good enough to use for the current regulation.
I.e. to save the highside current monitor and use the monitoring output as "is" value for the current limit comparator.
I wondered too. The current monitoring is not great, it only gives you a rough indication, it's +10%/-5% accurate. I don't think it's going to be stable with temperature either. The current limit is reasonably stable from 20 degrees C and up to 100. From 20 degrees C and below it gets inaccurate and that's why the spec is so bad on the "electrical characteristics" table. (look at the "Programmable Current Limit" graph, LT3081 datasheet). For bench power supply purposes it would be okay unless you want to do a really proper job and you want to compete with good commercial units.
TL,DR: The current limiting feature is good only if you use it on the 25 to 100 degrees C range. That might apply to the voltage regulation as well, in general, try to keep the device at a constant temperature, maybe with a fan, and you should get stable settings after the thing warms up.