I mix dough in my kitchenAide all the time, and this happens all the time, so through the process I check the consistency and dryness and I've developed a feel for the "just right formula", but being ADHD I don't go in with precise measurements each time, but that would be a good idea once perfection is found. So anywho, I take a strong spatula from time to time and cut it of the hook, to give it a nice restart with hook on outside of dough ball. but your dough needs to be dry enough that it is cleaning itself off the bowl and it will the hook too. It's designed to find that perfect balance so that it starts wet and sticky and then as the gluten starts to web it becomes self cleaning, and the kneading is drying it a little or maybe the material is absorbing the liquid, either way it goes from dry to wet. Another thing I do if the hook is wrapped in dough instead of working against the sides, I briefly turn up the speed and that will throw the dough to the sides and sometimes clean it.
From the sounds of it, because you were using it for a rather dry dough, it might've had to work more than it usually does, and could have resulted in some grinding of gears.
Now, if the mixer completely bogs down, most Kitchenaid models have a sacrifical gear that's made of plastic that will get destroyed close to the motor (ie, up top, not near the planary action bits near the bowl), but it's possible for it to not be quite bogged down enough for that to get destroyed.
As for servicing them, they're actually pretty easy to work on, provided you keep track of the parts and have a set of lock-ring pliers. (and if you open up the gear box up top, some grease to re-pack it).
When I helped service a friend's 600, we found plenty of manuals online; but be aware that there's more than one model of 600. (mine had a different model number than hers).
I'd personally try to check the planetary gears, and check if there are more shavings in there -- if so, it's a problem and at the very least, you need to empty it out. If I recall correctly, you don't actually need to open up the main housing -- there's either a pin you can punch out, or a retaining clip at the top of the shaft that you attach tools to, and you can remove the cover without too much difficulty. (I think it's the newer models that use the retaining clip; see the manual I linked to for those that use a pin)
The other gearbox up above isn't going to throw shavings -- it's packed in grease within a sealed case, so if there are shavings, it's going to not get thrown free (instead, it'll continue damaging the gears)
Best Answer
It is usually stuck because of fresh or old food particles getting into the socket or release mechanism
The simplest way is to drizzle boiling water onto the release mechanism. A few large pours over some minutes may be required to soften and remove the food particles
A quick spray of silicone oil may be required after this as the boiling water removes all factory lubrication too
Unplug the machine first! and take great care not to get water into the motor or electronic parts. Position the device over a sink or bucket so that water will flow away from the motor and electronic parts