Try contact paper

Take out inner door panel and replace with lattice.

You can install paintings inside the doors behind the glass

ASV called it.

I like ASV's idea. I've also been saving this photo due to having the same problem. Our need though is really just for the remote to work - the speakers are all outside the cabinet.

The wood in our unit is sort of a dark cherry so I'm debating which shade of latice to use.

Hi OntheFence - I think you can find it in most colours, perhaps a dark or medium grey? and also the remote works through it. Hope that helps

There is technology that exists and it's called a "repeater," that allows remotes to work through the usual wood and materials of built in cabinetry.

Thanks for all the great suggestions. I am going to try to try the lattice. The suggestions also made me think of trying grass cloth in the space.