Just installed a new 440 source starter. Started the motor (hot) and ran it for only about 10 seconds, shut it off and starter kept cranking the motor over even with key out. Quick disconnected the batt. Reconnect and the starter would engage again! Let cool for a few hours and everything fine.

R&Ring the starter is a royal pain due to headers.

Here are my thoughts to hopefully prevent reoccurrence.
1. Loosing the two mounting bolts to see if there is any slop, retighten bolts while pushing starter away from flywheel to gain any possible clearance.
2. Inspect starter relay to try to determine if there is any way the relay actually stuck closed…probably not likely but?
3. Drop bellhousing inspection cover and lightly grease flywheel teeth…..don’t know if this a bad idea or not.

Maybe it will all loosen up a bit with use.

Any thoughts?

Interesting...initial train of thought is that either the drive isn't retracting the pinion, or there's a bind resulting in the same thing.
Second thought is whether the drive is getting a signal to retract, or not. But why would that suddenly degrade ?
I can't recall anyone greasing flywheel teeth, but maybe looking at them some witness marks might be visible that indicate a bind/misalignment.
That said, I can't recall any of my Mopar starters, numbering into the 20s at least, plus dozens of friends' cars, having a binding issue; they seem more locked into position than SBC starters, for example.
Best test for pinion retraction would be in a bench vise - not the fun option, sounds like - but that may be necessary.

I did bench test the starter before install and it acted fine. Drove the car a little prior to this problem and it was fine, but never fully hot. This was probably the 8th-10th start since install, and the hottest (after a long slow crawl into car show).

I've more than a few vintage blocks (BB & SB) that the edge of the starter hits the block where you can't see behind it. Then the starter won't set flat on the trans surface. It's hit or miss. the starters don't vary. But the blocks do. Last one I had was a 360 Magnum.
Doug

if the starter keeps cranking I'd suspect an electrical issue. one can disconnect the relay lead that energizes the solenoid. then just touch the batt cable to the post and see if it starts cranking.
If it does you either have a shorted solenoid wire to the battery cable or the solenoid itself is stuck in the energized position.
the above should be visible dropping the inspection cover to see if the teeth are enagged with the flywheel. Could be and interference issue but it's not something I've ever seen on a Chrysler product. maybe Ho Chi min strike again?