I have this working now; the problem was not a defective LM317 (tested in isolation & within spec), but rather a careless assembly error (I placed 121K for R1 instead of 121
).
I have now discovered something about the design that I hadn't realized, so I record it here in case others are also implementing this circuit. I thought that reduction of the feed voltage from the specified (+28V to 38V, -28V to -38V) would only limit the maximum output voltages, but there's more to it than that.
Fed with (+15V, -15V), for example, the output gets up to (+12.99V, -12.98V) reliably, and even tracks sloppily up to (+13.44V, -13.23V). At the other end, though, the minimum output is a little more than (+2V, -2V) [tracking is good to (+3.00V, -2.99V), but at the bitter end the output is (+2.03V, -2.11V)].
A feed of (+20V, -20V) is almost enough. The negative output neg-mirrors the positive output to within <0.5%, from <+1V up to ~+16V; tracking is lost at the extreme upper end (+17.37V, -16.86V).
I got the PCBs for this from OSH Park, so I had to get 3, when one was enough. The PCBs cost me $6 each, and I'm happy to pass my two spares on to anyone who'll pay that + postage. Warning: I put the LM317 & the LM337 too close together, so one of them will accept only a Dremel-trimmed heat sink.