I’m not sure if this is truly original, but I have never encountered anyone defending either of the following two versions of the A-theory of time. Possibly because they are so wildly esoteric as to stand on the periphery of intelligibility. To explain them, let’s begin by thinking about the properties of Presentism, and C.D. Broad’s growing-block theory of time. On Presentism the set of things which exist is identical to the set of things which exist right now. Presentists think that there are no real future events (the future is not ‘waiting for us to get there’), and past events have literally gone out of existence. To become present is to become, full stop. On such a view not all the A-properties distinguished by J.M.E. Mctaggart in his famous essay The Unreality of Time are instantiated. It seems that a prerequisite for an event to literally have a property, such as the property of being ‘future,’ is that the event has to literally exist. If a thing literally fails to exist then it cannot literally have properties of any kind. Similarly, on Broad’s growing-block theory of time, things which are present come into existence at the present, and they continue to exist even once they have inherited the property of being ‘past,’ but future events do not literally exist (or have A-properties) at all.
Keeping these in mind, here are two other views. Since I’ve never encountered them in the literature before, I will take the liberty of giving them names. Let’s call them Apresentism and deteriorating-block theory, respectively.
On Apresentism events bear either the A-property of being future, the A-property of being past, or both, but no events bear neither. In particular, no events bear the A-property of being present. This is because the present, on this view, literally does not exist. The category of the ‘present’ is simply a heuristic tool, a useful fiction, but what it picks out is events which have both the A-properties of being past, and the A-properties of being future. All that ever really happens, on this view, is that events go from having exclusively future A-properties, to having both future and past A-properties, and then finally to having exclusively past A-properties. Is this view logically possible? I’m not inclined to think that it is, but showing what, precisely, has to be wrong with it remains a tall order. If one can show what is wrong with it, then I suspect one will be able to show what is wrong with presentism, but this is just a philosophical hunch.
The deteriorating-block theory is exactly what it sounds like. In place of events having the A-property of being present, and then inheriting the A-property of being past, but never literally having had the A-property of being future (so that layers and layers are added on to the world as the present rolls on), this view suggests that events have the A-property of being future, or the A-property of being present, but to become past is to fall out of existence entirely. Thus, the future is real, the present is real, and the present represents a sort of ontological precipice – events which cease to be present cease to be.
 Here’s a quick thought – on presentism construed in the most ontologically conservative way, God would, even if Sempiternal, not literally have a past or a history, anymore than any of us would.