If you are going to measure the brake shoe thickness wear, it is generally done where it is worn the thinest. From the picture, it looks like the shoe on the left is worn thinner than where you measured the thickness.
Greasing a friction material is a bad idea. The shoes are porous and grease can soak in, particularly when it gets hot. Hot grease flows into any crevice it can find, and its goal in life is to reduce friction. If your rear brake now seems ineffective, you'll have a pretty good idea of why that is so.
I have no way to judge how much grease you put on the show or how effective your method of removal has been. You'll have to do that. But, if you clean it well enough, you can test for effectiveness easy enough. If you can lock the rear wheel with foot pressure, it's probably good enough. I probably wouldn't want that situation on the banked walls of Daytona, though.
I can tell you what can happen if you don't get the grease off the pad. I had a car with a leaking bearing seal and the grease made a few drips onto the drum. Where the grease had dripped, the drum got very hot, much hotter then the rest of the drum, which changed the steel's temper and formed hard spots on the steel. These drums could not be turned true, as the hard spots were harder than the lathe's cutting tool. The hard spots had to be ground out of the drum and when the rim was finally turned true it was past it wear limits and had to be scrapped. That was my lesson on why it is bad to grease the brake drums.
If your bearings spin smoothly, you check for wear when the wheel is on the bike. You should not be able to move the rim sideways.
All the axle related parts need a coating of clean grease. The cavity does not need to be stuffed.
Cheers,