Gathered all the smaller hammers.
Only used the plastic head hammer.
It worked perfectly, along with a piece of wood used to reach the inside of the lids.
After the repair.
It's not perfect but much better.
The lids now line up the latches well and close easily.
Not going for perfection.
This is functional and close enough.
Here's what it looked like before the repair.
Pretty severe denting...
Due to the dents near the handle bracket, the latch in the picture doesn't really line up and the top lid is not parallel to the bottom lid.
After cleaning; before dent repair.
There's a couple of small splits in the lid's aluminum but should be OK as long as the box is not overloaded.
Could epoxy aluminum patches on the inside of the lid but not really necessary since it won't be too heavily loaded.
The inside of the lid showing the location of the small splits.