Well, that was some fun research. Natively, HSL isn’t supported by GameLab, but there is a cool formula that was created some time ago that will allow for the conversion.
In this example, I randomize the Hue between 0 and 100 and then keep the S and L at 100% and 50% respectively as per your original proposal. Then I set that to be the background color. It appears to work.
Up to you to adapt it to your project!
Good luck! I like your thinking and would love to see how you implement it.