Yes, I'd for sure try to put his tank on something much softer- but you'll have to leave room for the heat matt, obviously.
The easiest thing I can think of is to use hi-density foam weatherstripping on all the bottom edges of his tank- but leave a small gap for the UTH cord. Hardware stores sell it- it's sold in a flat roll, typically, & won't break the bank. I use it on the bottom edges of all my tanks anyway, because it keeps them from sliding off cabinets. (I used to live in the land of big earthquakes, Southern California, & it really saved my tanks, not to mention my snakes, but I still like using it so that no tank is sitting on a cord- that wears them out.)
Anyway, it comes in different sizes & is peel & stick- EASY!
Like this > > > https://www.homedepot.com/p/Frost-Ki...734H/100047977
Poor little corn snake...you too! All that vibration!