SA hubs have two drive torque outputs via freewheel ratchet mechanisms. 2nd and high drive via the right side ratchet, and low via the left side ratchet. If it's slipping in all gears, that would mean that both ratchets aren't working, which seems unlikely, so I'd look elsewhere. Before you do anything else, use a chain whip to torque the sprocket and make sure it's not slipping on the driver. It engages via 3 tabs which might have worn or sheared off.

If the sprocket isn't slipping and the driver is slipping w/respect to the shell, then something is keeping both ratchets from holding. Field strip the hub and without assembling hold the mating ratchet assemblies in your hand and check that they work cleanly and crisply, and that when you load them the pawls don't try to move inward and dis-engage. Wear on the ratchet ramps, or the tips of the pawls can cause this. So can anything filling the ramp area and keeping the pawls from pocketing properly (though I assume you cleaned them).