Sew-Classic has craft syringes and you can also buy them hobby shops. Most have a curved tip you can cut to just the right diameter to fit inside the hole on the Singer grease tubes. Then just fill the syringe from any bottle of p-j put the plunger back in and inject it into the motor.
I have so many partial tubes of the original Singer Motor Lube in the tube I'm not hurting. But were I to run out I'd give the p-j a try. It works in my White made machines, why wouldn't it work in a Singer?
And Rodney, you might just have something there.
Joe