In your video, it's pretty obvious the upper motor is relatively quiet while the bottom one is making quite a racket. So I would go after the lower motor. Some motors have carbon "brushes" that rub against the armature and wear over time. Many modern motors don't have brushes, but if yours does it could be one of the things that it needs. The noise though makes me thing the bearings/bushings are bad. If it's a bushing, you can sometimes get more life out of it with some oil. If it's a bearing motor, then the bearings would have to be pressed off/on and it's pretty involved.
Once you remove the motor, you can inspect it for bad bearings, loose parts, etc. Also, you can google the part number on it and see what your options are for replacement. You may even be able to take it to a furnace company to see if they have a replacement. If so, you could have it back together in a day. Otherwise you could be in for a wait in which case some space heaters are a good idea. Just be careful in how you use them.