Kp2671 quits spinning under heavy load and making a grinding sound. What part might it be?

It sounds like either a partly stripped gear or a broken driving pin. If it is one of those options though I'm surprised it has not stopped completely.

there could be a thermal over load switch that you may have to press
if there isn't,take it in to an appliance repair shop for a look and quote

Let it completely cool and then start again. It overheated because your speed was set too low for the heaviness of the dough. I have burned up three kitchenaid stand mixers so far making bread. go up one setting at least; if it is straining, go up another.

I have fixed many mixers with the same problem. The only part that consistently wears out
is the Worm Gear Follower located inside the Transmission housing. The teeth are wearing out
and becoming chipped. The grinding noises you hear are made by the Worm Gear and the
Follower. As time goes on, the metal filings from the damaged follower will eventually destroy the Follower and the Planetary will stop rotating.
Sooner or later that gear need to be replaced. Also remember to use new Grease after
a new gear replacement (metal filings from the old gear will damage your new gear)

Its worth fixing but having someone who specializes in your product is the key, these machines are wonderful products and engineered great. I would say if your mechanically inclined jump on inside the machine and see whats going on, but if your NOT send unit to us USPS it's not that expensive plus you would only have to pay oneway, we will take care of the shipping from our side,,estimated cost $29.00-$49.00

it could be the bushings
but i would suspect the plastic gears

Disassembly and inspection is the only way to verify what it is. It sounds like you are correct. I have bought parts very reasonably on line and repaired our K/A mixer. The better sites ( I think I used appliancerepair.com) have exploded diagrams. If you are tearing into yours, these are invaluable, and when you get to the broken part, you'll have a name for it.

Best regards, --W/D--

I replaced the control board on mine, and that seemed to resolve the issue

this is common for any device that has a motor,either the gears are grinding or the motors contact brushes need replacing, it will have to be looked at to determine the exact cause

the company jumped right in and helped me out. impressive.