I wouldn't replace a well sorted ALWSR with a TPR'd LM317 based regulator and I've built quite a few of both though not specifically the TPR4. However there are some quite significant and straightforward improvements that can be made to the original ALWSR circuit. I would recommend R-C filtering the supply to the Opamp (a resistor between OP2 and C3, making sure C3 is at least 22uF). This involves cutting a track and checking the current draw off the opamps data sheet so not too many volts are dropped.
I would also recommend splitting R4 into two series 5k resistors and filtering their middle to SRIN with a large electrolytic, say 47uF-100uF. This makes for a stiffer CCS.
The TPR on the ALWSR circuit can be improved along the lines of the Acoustica TPR mods by removing C9 altogether and replacing R1 with a red or green LED and reducing the value of R2 from 1k to circa 240 ohms.
Finally the ALWSR is more stable when C1 has high ESR, C7 is not fitted and C5 is fitted (after the Opamp supply is decoupled) with a high ESR capacitor, say greater than 10uF with 0.5 ohms ESR.
There are other mods you can do to the reference voltage and the current source if you have enough voltage headroom but these ones above will give you a taste of the improvements available. What are your ALWSR's input and output voltages and which Opamp has it got?
http://[URL=http://s869.photobucket.com/user/John_Luckins/media/ALWSR%20ve%20circuit_zpszwjgx97q.jpg.html][/URL]
You could do these mods while listening to the TPR4 in there and then swap the ALWSR back??
John