First thing, if your engine lost time and struck a valve, it's bent. If you were going at highway speeds, usually above 60mph, if there is contact, the rod will bend.
I agree, there is no way a belt should be installed and 'keep your fingers crossed', because its not usually 10,000 miles. It's usually 500 miles and a valve head breaks off and ruins whats left of the head, tears up a piston and rod and may ruin the cylinder.
Under water loss situations, there is most often a problem with heat warping. This most often occurs on the cylinder head, but can also affect the flatness of the block.
Piston rings and cylinders are usually not affected unless the heat is very high.
However, I would be checking out some of the rod bearings and maybe the mains to check condition.
BTW: If you had only a quart in your radiator, your 'no radiator alarm' issue could be that since you had no water hitting the water temperature sensor, it was not registering.
Usually, before you get a overheat light, you get a 'low water' light. I'd be checking to make sure that works.
We do this job regularly if you need any further assistance. We just happen to be in the same State