When you say dripping out of the bottom of the seal do you mean the gasket between the third member and housing?
I had a leak that I thought was the gasket and it ended up being the fluid was wicking around one of the four bottom studs that are under the fluid level seeping around the knurl that retains them
I had that third member out three or four times before finding that, it took some Mopar brand grey transfer case and rear end sealer on the knurls to fix it It would leak around the knurl ands leak out behind the flat washer and nut and look like it was leaking from the gasket
Good luck, let us know what you find and do to fix it, you can fix it