EDIT -- Never mind, I see you replaced the cogs. Are the chainring teeth excessively worn down? But it would be unusual to have the big ring get that worn out.
It doesn't sound like a hub problem to me. If the hub had slipping problems under load, it probably wouldn't work at all, just spin freely all the time.
Are the cogs worn out? If they are really worn, and you use a new chain, the chain could jump a tooth when pedaling hard. They'd have to be very worn out, though.
From Sheldon Brown's Chain Maintenance page:
The illustration above shows two formerly identical sprockets, viewed from the right side. The one closest to us is badly worn. On a new sprocket tooth, the surface that the roller presses against is perpendicular to the pull of the chain. The worn teeth have become ramps, causing the chain to ride up under load.
In addition, as the roller follows its tooth around the sprocket it rolls up the "ramp," while under load. This promotes wear to the insides of the rollers and to the "bushings" they roll on. With a properly meshed chain, the roller only turns a tiny bit as it rolls onto and off of the chain.
Due to the pitch mismatch, the chain will not reliably mesh with the sprocket under load, and will tend to jump forward, skipping over the teeth.