Those brackets look very similar to mine as fitted to my 2011 +4. I am not aware of any changes to later models and don’t think I have seen new racks being marketed for newer models either.
If I plonk my rack onto the pegs, there is a good half inch gap between its central point and the boss on the spare wheel, but it with light hand pressure, the gap easily closes up. Looking at the bracket “platform” on which the pegs are fixed, when installed, it looks almost level but a closer look shows it very slightly downhill at the front.
Could your issue be this...when you remove the T bar, it is very easy for the wheel to slip downwards un-noticed. This has caught me a few times. Just make sure that the wheel is pushed up tight against the serpent’s head brake light and everything should drop into place but you may need to spring it a bit (not so much as to bend it though!)
As far as greasing is concerned, yes on full lock you will invariably restrict access to the lower nipples. Simply turn it back a part turn and it’ll be easy.(effective greasing does not call for a totally full lock position; its just that turning the wheel makes it easier than in the straight ahead position)
Hope this helps.