It is the convection fan that is noisy. I have a convection oven, and
it's only noisy when the convection fan is on. If you use it in normal
oven mode (with the heat elements, no fan) it is quiet.

A convection oven uses a fan to circulate hot air. You can have the
broiler on at 500 degrees, and the broiler element is right under the
electronics, but if it's not in convection mode, you won't hear the
fan.

I'm not sure how Dan's oven works, but at least mine works this way.
Regular ovens don't have fans. Convection ovens have fans inside the
oven to circulate hot air.

Convection ovens do cook food better and faster.

I think QuietRock could solve the problem. They have a QuietSeal
adhesive for the panels. Just keep in mind, it's about $100 for a sheet
of this special dry wall, but it works.