The difference is that the LT108x enforce their SOA much earlier than the LM317. so when you are starting into a bigger load, the differential voltage between input and output can get big enough that the regulator starts enforcing its SOA, and limits the output current to about half an amp (see the 'Short-circuit current' diagram in the datasheet). It took a while until I discovered what the problem was. The datasheet claims that this should not happen, but my experience was otherwise
How does the datasheet claim it should not happen while including SOA data in both the specifications and curves?
The difference is about 7.5 versus 15 volts but the LM317 has almost twice the junction-to-case thermal resistance making up for this. Under the same conditions, the current limit curves are actually better for the LT1083/4/5. The guaranteed tested curves are lower but I suspect this reflects a more conservative attitude because the LM317 datasheet does not even include them.
The above reflects my biggest complaint about 3 terminal and most integrated regulators. Without a separate current limit adjustment, the peak current is much higher than the sustainable continuous current in a variable output application. I would be nice to be able to parallel multiple regulators to lower the junction-to-case thermal resistance without raising the total current limit.
I'm really interested in any circuit suggestions and maybe try things out and see how it works.
The LT1033 and LT1085 datasheets have some application notes worth studying.
I see that the LT1085 has very similar circuit configurations (even the 240Ω resistor which I've read somewhere that should be 120).
This resistance sets the current through the output divider. 120 ohms is commonly used because 1.25 volts / 120 ohms is 10.5 milliamps which is higher than the minimum required load (10mA for the LT1085 and 5mA for the LM317) under all conditions. If an external load is always present, then this resistance may be higher.