Eternity is outside the presence of time, not just from now to forever. Though eternity clearly doesn’t end, it also cannot have a beginning. It is where God Himself dwells, and therefore there is no beginning. Therefore, a person in time cannot be eternal; rather he can enter into eternity and eternal life.
Your distinction about eternity being “without time” is interesting, however perhaps not supportable. Only God is timeless. The self-existent attribute of God is called His Aseity (from two Latin words “a” and “se”, meaning “from Himself”). His personal name revealed to Moses in Exodus 3:14 is “I AM”, a simple statement of being.
Time is a created dimension. It is perhaps best defined as a succession of causalities. Time was created as the canvas upon which God paints His unfolding will. As created beings, humans will always be in time. All created beings will have an everlasting existence—fallen and unfallen angels; believing and unbelieving humans. Revelations 20:10, using words of time, says that those following Satan will “be tormented day and night forever and ever” in the second death—eternal punishment.
Eternal life and life everlasting are both sequential. Eternal Life is life of the quality of unending relationship with God. Revelations 21:25, again using words of time, describe the gates of the New Jerusalem in the following words: “And in the daytime (for there shall be no night there) its gates shall never be closed.” This city is a new creation by God, still within the causality of His will. Eternity is an infinite amount of time. Its uniqueness is in the term “infinite,” rather than absence of time.
I think your distinction does correctly point out that the believer's perception of time will alter. We will be different, but still material and temporal (bound in time) in some ways. Today, we are locked into night and day cycling, birthdays, longevity, all of which dominate our life. When we are with Christ in the new heavens, we will be in resurrected bodies and light will remain as our surroundings. We will be busy in worship and carrying out His Kingdom will. Time will remain a reality; however, we will mark the passing of our lives differently. Mathematically, “infinity plus one” has no meaning. Infinity plus anything is infinity. In the same way, it will be meaningless to talk about “how long we have been in Heaven.”
For more information on the subject of Heaven, see Randy Alcorn’s book Heaven.