This problem has been around in various Singer machines since at least the Golden Touch & Sew 750 (in 1972!) - maybe even in a few earlier ones.
I'm sorry - I know how frustrating it is. My Mother's 750 just about drove me to drink and my Futura embroidery machine is just as problematic - it's spent more time in the shop than it has embroidering. :?
If you only have time for quilting every now and then, I know you don't want to spend that time fiddling with the machine.
I would look around on craigslist and find a model 15-91 in a good solid cabinet. The heavier, the better. Spend $100 or so on that and then put another $100 into having the motor re-wired and buying replacement cord, light and foot control. You will have a wonderfully simple straight-stitch only machine that will give you perfect piecing seams and when you're done piecing, will do beautiful free-motion or machine driven quilting.
Some people kind of wrinkle their noses at the old machines and that's okay - not everyone likes the same thing, but if your sewing time is limited, the simpler machine is going to help you make the most of that time and give you the fewest problems. And you could find that the simple maintenance and cleaning is a soothing activity and very rewarding to take a dusty old cast iron machine and turn it into a smooth-running, shiny retro piece. :)
Good luck! :)
Elizabeth