It's been too long since I owned an SX-117, but one source of 60 Hz hum is inductive field-flux coupling between the power transformer and audio output transformer, including any inter-stage audio transformers. Back in the day, hum/buzz problems were largely masked by the limited frequency response of Hi-Z headphones.
Two examples: Collins 75S-3A and the solid-state Hammarlund HQ-215.
The Hammarlund hum problem was so bad when using modern headphones, that I gutted the entire AF section and constructed a class AB push-pull amp in its place. In the original design, the power transformer is placed adjacent to two audio transformers. Even after moving the transformers on the chassis and re-routing cabling, enough hum remained that that it was intolerable to me.
Similar problem with a Collins 75S-3A. Although my Collins 75S-3C has zero hum issues, the 3A's output audio transformer is also placed near the power transformer. You can remove all audio going into the output transformer and 60 Hz hum is still there and it's not in any way related to headphone jack bonding. Instead of a re-design, I simply took the AF control wiper arm contact and routed it with RG-316 coax to the receiver's rear panel "spare" RCA phono jack and bypassed it with a 0.001 uF cap. When using the 3A, a separate audio amp is used with much better performance than the original design -- and no hum/buzz.
When the chassis is used as a tube's filament return, the entire chassis has 60 Hz current. What we may think is a safe grounding point often isn't. In these cases, hum can sometimes be reduced by re-tightening a tube socket's ground ring to the chassis. I think better designs use balanced twisted filament leads to keep 60 Hz currents off the chassis -- and a means to control 60/120 Hz current from a power transformer's center tap by segregating grounds, then bringing them together at one point, away from high-gain audio stages.
For me, tracing hum and buzz is one of the most difficult parts of a restoration because there are so many ways for it to affect an audio circuit.
Paul, W9AC