I can see why your are glum.
My machines have made truck loads of transformers. With out a counter I don't know how to get the exact same transformer every time 8 hour/shift.
A round pot core is very hard to hold in a winder.
The force to bend #12 wire is equal to the force to break a pot core bobbin. #12 is no good at high frequencies.
Breaking bobbins is one of the problems I was referring to, and slipping with round bobbins, which nearly every core used in High Freq smps design is!
Multi strands of smaller gauge wire one can do, but the winding machine is somehow not so helpful with multiple strands. Maybe with more modern bobbins, you can solder to the pins first, then wind smoothly; but to perfect wind from layer to layer with multiple strands is tricky. In general, I found that the small number of turns made machine winding awkward, since getting started and terminating is a big part of the problem!
Maybe the factory machine (I'm assuming) you use works better, but is it "cheap" as FusionITR originally was asking?
If it is for a small amount of turns of large stiff wire, maybe a hand cranked machine would be a good way to go? You can still get those small hand cranked drills that are perfect for low speed and precise control.
I still use my hand cranked drill on large holes in some plastics as you can turn it forward and back and get a lot of control and torque.