You got two issues going on here:
1. Motor: Okay, good, you replaced both brushes. Are you sure you did not get any oil on the brushes when you replaced them? Brushes have to be dry, absolutely dry. It sounds like the motor ran before the brush replacement issue so my best guess is the brushes did not get seated correctly when you replaced them or they got contaminated with oil or even grease.
2. Heat: The reason for heat is the oil thins out with heat and then the oil can seep down into all those itty bitty nooks and crannies. One little piece of rust can stop the pure, smooth motion you are looking for.
PS I don't use Singer oil. I prefer TriFlow oil because it contains other lubricants the Singer oil does not contain. Triflow can be found at most pro bicycle shops and online. Also, Triflow comes with a needle nose applicator that allows greater access to all those nicks and crannies.
Shari