I took it apart again and found a suspect issue... the winding shaft was attached to the spring barrels by two small set screws that went through each side of a collar on the first spring barrel. If the set screws weren't exactly lined up with a very small hole through the winding shaft, they would allow the shaft to slip inside the spring barrels. This looked like a poor design, so I took the winding shaft out of the barrels and re-tapped the holes in the collar to #8-32, then drilled the hole in the winding shaft to 3/16" so a #8 bolt would go straight through from either side. I put the barrels back together and installed the winding shaft, fastening it all the way through the collar with a #8-32 slotted bolt, eliminating the set screws. Then I re-installed the barrels in the motor and put the motor back in the machine, wound it up and it worked perfectly. I was finally able to play a record on this Lauzon phonograph for the first time in 4 or 5 years!!! Now, all it needs is an adjustment to the speed control and some green velvet on the turntable as originally installed, along with some grill cloth...
There is finally light at the end of the tunnel...

Thanks again to Forum member Ken Brekke for his help and generous donation to get this machine working again...