What do you use to keep high gloss speakers clean?

The first step is definitely dry Swiffer.

It is the dust (grit) that causes the swirls when wiped.

Same, car wax. 

Fresh, cleaned, water dampened cotton washcloth, followed by a dry cotton towel. Nothing else needed. Been using this for decades without the need to add any "product" to the process.

Don’t dry dust ever. Dry dusting is what causes the micro scratches in the first place. If you never cause the micro scratches, you never have to add product to cover up, or polish out the micro scratches.

I second the McGuire's Quick Detail.

For wood I use  Z's Wood Nectar. 

Nova 1

ozzy