In all honesty, I have trust issues which is why I see one thing that is blatantly untrue with a person - I automatically distrust anything else from the same person unless it can be proven otherwise. It MAY be fine. It might be a great product. I don't know at this point.
How much you use in your motor will be determined by the grease tubes. The best way to learn about that part is by following Rain's tutorial here:
http://vssmb.blogspot.ca/2012/01/com...ted-motor.html
ETA: I just re-read part 19. (It's been a long time since I followed the posts but I've recommended then to people over the years) Add him to the list of people who recommend PJ. 
Steps 9 and 19 will be the relevant ones but I find the whole tutorial worth reading because you'll learn a ton about your motor. Far more than I want to type out here.
Ideally, I would clean out the lube and clean and inspect the worm gear and commutator, etc as Rain shows in the tutorial. It's the only way to guarantee a good result. Consider that there's a good chance there's still some of the original lube in there is up to the age of that motor - potentially over 70 years old.
The Singer Lube you just ordered - if it's white like what I showed on the previous page - should still be suitable for gears (though it's not my first choice of greases for gears either.)
DH brought up a good point as to a potential why as far as the US and UK formulas having different melting points:
"Back in the day", most UK countries would a lower average indoor temperature for most months than say Texas in the summer. In the years before AC, I bet in parts of Texas a tube of lube that melted at 115F might have been liquid in the tube. That would not be fun to try to get into a motor - especially a potted motor.