You could still feed it with better filtered DC instead of AC. Noise wise that will probably not do much, but you may get rid of the 60 Hz multiples.
The 60Hz multiples are not an problem in practice. I don't know why Amirm's setup has this issue, specifically. Perhaps measuring the noise with the input shorted might resolve the question.
As I wrote, in my measurement system I have to attenuate the signal from the generator, in this case using a "rotated pi" (A large R is series with signal and ground, a small shunt R between, in the order of 330 - 1000 ohms and 10 ohms) to make noise and distortion measurements that are consistent with the intrinsically floating cartridge source.
The phono inputs should never have any signal/supply current flow through them. Proper operation depends on the source being fully isolated, which is true of phono cartridges that are not connected to chassis ground. My RME box does not have a fully isolated generator, so the impedance in series with the output has to be sufficiently large that the current flow back out of the phono input into the test source ground is low enough to not create a "ground loop" of sorts, and the attenuation allows a large source signal to be produced, which also helps. The RME box is not isolated. The outputs and inputs do not have a fully broken ground path between them, so provisions had to be made.
The phono inputs are not connected to chassis. The output grounds are connected to chassis and also to the ground lug. The chassis is best grounded to the follow up preamp via the phono cables and the TT ground (isolated from the cartridge signal wires) should be connected to the chassis via the lug.
Sota wanted a system that was cheap and did not use switchers of any sort, but there are two levels of regulation and a hefty amount of post rectifier filtering so the use of a half wave rectifier was inconsequential, and an inexpensive wall wart could be used. It's similar, but not identical, to the approach used in the Mani-2.
The original DIY design used a switched mode supply and filtering to generate the internal +/-15v rails directly from mains.
The hum/ripple on the supplies is almost unmeasurable and the circuit PS rejection is high. It actually does get hum components that are c. 96 dB down from the rated output of +5.5dBv, which is with a 10mv MM or 1mv MC input.