ok if i understand you correctly the grease should be sticky enough that it doesn't leak ? well in my case it doesn't seem that way seems like gear oil too me it drips out when it sits for extended periods, this is the way it came right from the dealer, is it ok to use an automotive type gear oil?
The reason I asked for the factory number was to get an exploded view of your gearbox. It's an assembly so not broken down.
You understood correcty.
You don't know what grease is in there or how much. The factory could have loaded with paste or oil grease. The dealer may have topped off with one or the other. It's tough to put in past grease after assembly so someone along the way may have added lighter grease. You could use auto EP grease but better oil or paste greases are not that much more so not a great saving over using better greases.
Since the machine came with the seal out can't you go back to your dealer? If not I'd try pushing it back in.
You could open the fill hole and stick something in there to try to gauge how much grease is in there and what type it is. Clean off the gearbox and see where the leak is. If the leak is not from the gasket area and only from the auger seal then you would at least have from the seal down filled with grease (assuming it's not paste grease). The gear will still be picking up grease. Some liquid grease would eventually find its way over to the seal but that would probaby be a very slow leak and you could live with it.
Other than that you could pull and open the gearbox and put in a new seal and proper grease.