As I’m sure you’ve figured out, the icebox on the 424 isn’t very well insulated. Fixing this could be very difficult and time consuming since you’d have to lift the countertop and basically fit in a new icebox. You would end up with a smaller icebox. Several owners have done this. If you do nothing else, replacing the lid with something better insulated is recommended and fairly easy to do. The stock lid hinges in the middle. You need to remove the lid to get almost anything out of there so you need to clear off some space to stow the lid; a frustrating process.
Here’s what I did. This replacement is well insulated.
https://www.pearson424.org/gallery/index.php/Interior-Modifications/rcarterinterior/P8180006
Rich