Wouldn't worry about where the grease is going on the gimbal bearing. It will follow the 'path of least resistance', so if it finds an easier path out through the back of the bearing rather than the front, that's the way it'll go...
To remove the yoke, uni joints, drive gear as an assembly, you'll need the tool for removing the lock ring. I see many people doing that (removing the bearing pack assembly), but I have NEVER had any problems removing and replacing unis in-situ. It's a matter of getting the yoke turned the right way.
Flick the C clips off (beware, they will fly around the workshop and never be seen again!). Then using a soft face hammer, knock the front joint (the one closest to the engine coupler) so it 'self-drives' one of the cups out. Pull that cup out of it's 'holder', then drive the cross all the way through to push the cup out of the other side. Do the same with the other section of the cross. You now have the front uni out and just the back on in. For this one I use a couple of sockets and a sliding F clamp. Use the sockets and F clamp to again drive one side out, pull the cup, push the cross back and through. Same with the other side.
Reassembly is almost the direct opposite of pull apart. Just be very careful about the small needle bearings inside the cups. Don't let any fall down.... Once you have it all back together, give them a knock with the hammer to 'centre' the cups and crosses.
Chris.........
(Yes, the next one I do I will video)