Potential ways to silence a (new) Sturmey Archer 3-speed hub

I have a new Sturmey Archer 3-speed S-RK3. It’s a standard 3-speed hub with a 9-spline driver and disc brake mount.

I use the bike with a belt drive and one of the benefits of the belt is the extreme silence.

Out of the box, these hubs tick in at least 2 out of three gears while pedaling along; that’s how they are supposed to be.

I’m interested to know if anyone has successfully muffled the ticking by using a thicker oil lubricant for the hub internals. I have previously achieved this on normal freehub/pawl mechanisms by using a thick oil like Lucas Heavy Duty Oil Stabilizer.

I am not concerned with voiding the warranty.