Since you think believers will have different levels of authority in Heaven, what do you believe about the Catholic and Eastern Orthodox views of Saints who have more access to God than the rest of us?
There is no implication in scripture that anyone has more access to God. We will all experience his presence because he is omnipresent, unlike man who can be only in one place at a time.
The Heavenly Father will welcome us just like an earthly father welcomes his child. But there will also be different levels of responsibility in Heaven which will require different levels of access at different times, though no one is ever excluded.
If a billion people needed or desired “extra” or “special” access to God at any given time, it would not begin to exhaust his ability to respond, since He is infinite.
For more information on the subject of Heaven, see Randy Alcorn’s book Heaven.