FrameStrata
https://wow.gamepedia.com/FrameStrata
Also it might be worth setting parent as MainMenuBarArtFrame, anchoring onto shop button, and hiding shop button with :Hide(). Might be a simpler way to do this than putting it in the center of MainMenuBar and moving it all the way over.
lua Code:
StoreMicroButton:Hide()
QuickJoinToastButton:ClearAllPoints()
QuickJoinToastButton:SetParent(MainMenuBarArtFrame)
QuickJoinToastButton:SetPoint("CENTER", StoreMicroButton, "CENTER", 0, -10)
QuickJoinToastButton:SetFrameStrata(StoreMicroButton:GetFrameStrata())
The social button is 1 pixel smaller in height than the other buttons, though. So it looks a little bit off compared to everything else, but I imagine that won't really bother you.