That's exactly what I would have expected. Most shops say that the Finish Line brand is an exact replacement for Tri-flow. Synthetic Lubes typically don't have a melting point - which is why we say not to use them in the motors. we -want- melt to have controlled lubrication of the bushings/bearings.
I wouldn't use the synthetic, even if I was disciplined enough to check once a year. A couple of reasons - I prefer not to disturb the motor wiring more than necessary and manual checks/lubing every year is a lot of disturbance for 50 - 80 year old wiring. 2. It's not likely to always be me checking these machines. One day, I won't be around for their maintenance - whether I sell the machine or start pushing up daisies. 3. Why cause myself more work than necessary?
You need a grease with a relatively low melting point - which means it will be an organic of some sort. I find it interesting though that the 2 places that seem to say "NO petroleum jelly" are the same 2 places that sell their own "formula".
Sew-Classic still recommends PJ: 4th paragraph.
I'm also going to try to pop into an electric motor shop and see what they say.