I have several owners manuals for I believe White and White made Kenmores that actually states to use petroleum jelly in the motor lube pots. So that is what I use in those machines and it works quite well.
For Singers I use Singer motor lube in a variety of vintage tubes. I've amassed quite a few. No two look the same as they come out the tube, but they work.
I haven't bought any of the newly made replica stuff yet, so I don't know how it works. And I've not used any PJ in my Singers as of yet. However I fail to see why it would not work as the Singer motors work on the same principle as the White motors.
When I rewired my first 15-91 I used Singer motor lube as the lube pots lube both the gears and the motor shaft bearings. That has worked well.
Somewhere back a couple years ago someone, perhaps here on the QB, did a test where they melted Singer motor lube, PG and IIRC Tri-Flow grease and measured the temp when it started to melt. The temp for this test was, again IIRC, 115 degrees for the Singer grease and PJ. The Tri-Flow of course never melted.
I do not know much about greases other than what I used in automotive applications. Sometimes, like in drum break type wheel bearings you need a grease that will soften up with heat and flow back onto the bearings. With disk breaks that run far hotter you need a more heat resistant grease that will not melt at as low a temperature.
I think sewing machine motors are more like the drum break bearings than the disk breaks. The temp is lower and needs grease that will soften up at a lower temp.. Hense the PJ as stated in the old White manuals or the grease Singer sold.
I do wish we could find a readily available source of grease that was the same as the Singer grease. It would sure make matters simpler.
Joe