Unless the grease is petroleum based, and many are not, oil will not thin it.

New Sturmey hubs are greased, but with an amazingly small amount of grease, only where needed, not filled.

The grease in new Sturmey hubs is a Semi-Fluid grease (NLGI grade 00). If this were any thinner it would be pourable. The best place to find such grease in in a large lawn mower service shop. I believe it is used in the gearbox of commercial mowers.

Thicker grease can keep the pawls from engaging, but most likely it's your indicator adjustment.

Are you sure the indicator is the correct length for your axle? http://www.hadland.me.uk/2tables.pdf

Many aftermarket indicators sold for SA hubs are off on the length, making it hard to adjust. (Sheesh, if you were cloning a part, how hard would it have been to get that right?)

BTW A few of my dozen or so SA hubbed bikes don't get ridden much. I'll be converting these to grease. so they stay cleaner.