Several things I'm seeing in your videos.
Rail nose is a little too high BUT you should still get better rebound than you're getting. Possible someone switched old rails for your newer ones. The rail rebound looks a little stiff, this is usual of cheaper tables. You can test with your fingers by squeezing the rail nose. It should sink in and feel rubbery. Hard rail rubber = poor rebound.
Slamming the ball onto the 1st rail will raise the nose and the ball will be momentarily "trapped" which slows down the ball dramatically. As you notice the 2nd & 3rd rail bounce is nearing normal.
Your photo of underside, your rails are made of pressed sawdust, of rather POOR quality I must say.
I've worked in cabinet shops, what you have is NOT solid by ANY means. We use it primarily as filler. That is another piece of the puzzle where you're getting poor rebound, it's not solid like oak or maple.
The noise is USUALLY from loose rails BUT you say they're tight. OK, so now you'll have to raise the rails to see if the cloth was stapled correctly (as others said, cloth relief). 1 or 2 layers of cloth raising the rail will act as a shock absorber.
SPEAKING OF CLOTH... if that blue is your cloth, I hope you didn't pay much for it. It "pills" pretty bad.
PM me, I have suggestion how to improve that cloth as it sits.
Take photos of your work. Before reassembling, we can give more advice.
BTW: I had a near new SEARS $50 table and REworked it so it performed reasonably well. Definitely better than your videos show.
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