boylesg, I think it would be useful if you looked at how the current is limited in this LM317 circuit so you understand why it isn't suitable when placed after the voltage stabilization.
The LM317 family are actually voltage regulators and the intention is to maintain constant current by dropping a regulated voltage across a fixed resistance. It works on the principle that I = V/R and if 'V' is regulated and 'R' is a fixed value, so must 'I' be a fixed current. What the circuit is doing is treating the resistor as the entire load for the regulator (imagine the ADJ pin is grounded) and to is trying to stabilize the voltage across it to 1.25V, the reference voltage inside the LM317. You can do the same thing with 780x fixed voltage regulators if you choose appropriate series resistors. No matter how you look at it, there will be voltage dropped in the LM317 itself plus up to 1.25V dropped across the resistor.
Brian.