My 12 year old impact driver seemed worn out so I replaced the motor. That fixed it. This is called cutting to the chase. Here's a link to the part I used. Motor Service Assembly 23-30-0090.
I did some more research into the physics of what exactly is happening in an aging motor. As far as I can tell the issue is that the windings in the motor have a failure of the insulation. They get crammed with carbon dust or other conductive crud which lowers the insulation resistance and pulls more current from the battery. This is why you aren't supposed to use compressed air to blow out a motor housing. All these extra amps are burned up as heat instead of turning into torque. This is basic Ohm's Law logic. Motors are supposed to have a really high insulation resistance. When it starts to fall off then the motor no longer does the same amount of work with the given voltage. None of the sources I found come right out and say this. But that's the manifestation of the issue for me in particular.
My research did reveal that the smell I associate with my grandmother's old Sunbeam mixer creaming butter and sugar for pound cake is actually ozone and vaporized graphite. When my impact driver started making that smell it made me hungry for pound cake, but in fact it should've told me the brushes were breaking down. I always thought worn brushes manifested as an on/off problem. Apparently this other failure mode is also common.
There's a film that forms on the commutator made of copper and carbon and water vapor. It requires the exact right amount of current and humidity to make this protective film that is constantly broken down and reformed. I expect my very humid climate and only using my tool occasionally made it prone to over-filming which lowered the resistance even more, burning off even more of my current as heat, running down my battery really fast without delivering enough torque to get the job done. And also making that smell that makes me think of butter and vanilla.
I have a lot of tools now that are brushless, substituting permanent magnets and microcontrollers for carbon contacts. I will miss the sense memory of my grandmother's kitchen, but I don't have a lot of patience for a tool that won't turn a screw hard enough to pull the work together.
I made a video to show what it's like change the motor in one of these tools. I could've edited it to make it look like I didn't screw it up, but I think that sends the wrong message. Everybody ends up with a part leftover. You have to accept that anything you take apart you're going to have to take it apart again at least once to put back something you missed. Shooting video of the whole thing really helps you figure out exactly where you screwed up.