I wouldn’t exactly call aeveternity the mean between time and eternity. Time is simply a measure of change, and since aeveternity consists of changes, it is very much time. It isn’t the same kind of time we have here in the material world, but it is time nevertheless.
The Greeks, in fact, had two different words for time, chronos, which is how we normally think of earthly time, and kairos, which is best described as “event time”. For intents and purposes, this is precisely what aeveternity is, event time, where the events measured are purely immaterial changes rather than material changes. The changes are not merely changes in choice, but can be any immaterial change, like the acquisition of knowledge. We know that angels are capable of growing in knowledge. I personally like to call aeveternity “kairological” time.
While united with our bodies, we experience chronological time. It would be incorrect to say that our souls experience aeveternity while still united to the body. I think that addresses the question of whether we can pray for ourselves from Heaven. The answer is no.
If you are familiar with the distinction between continuous and discrete numbers, I think it can provide a wealth of insight into the topic. Chronological time is continuous time. The number of changes which occur in the material world are infinite, and hence time is infinitely divisible. Kairological time (aeveternity), on the other hand, is discrete time. The changes in the immaterial world are much less frequent and hence time occurs in discrete chunks.
Just as there is an aspect of relativity in our time here in the material world, there is very much relativity (or perhaps more precisely subjectivity) in the aevum.