Can we do better than an LM317 for DIY purposes, and without getting too expensive?
I asked the same question. I found that most regulators used for audio circuits can't handle the SL1200's 40+ vdc input from the rectifier, but the LM317 will. I went with Linear Tech's LT317 which is a drop in replacement with performance closer to their popular LT1084-85-86 regs. At $4 ,the LT317 is 10X the price of a 40 cent LM317. I hope that's not too expensive for you.
If you go with a different transformer, one with a 18VAC secondary and 2 amps of current capability, the rectified voltage drops to around 25vdc (18 x 1.414). With that you could use a LT1085 or similar regulator.
I looked at the internal PS that Paul Hynes is offering for the SL1200. Since the motor drive demands the high current, not the control circuitry, he separates the two circuits and gives them each their own regulator. That makes a lot of sense.