To avoid confusion let me use beingness instead of being.
Like other things, if beingness also undergoes changes, we cannot name it beingness. If the word you used as 'being' depends on our sense organs, for convention you'd better say that it exists/existed for a certain period.
If we said that something had a beingness, we can no longer say that now it has no beingness. To test this, you can use your commonsense or refer to the Bhagavad Gita.
See: Bhagavad Gita 2.16
nasato vidyate bhavo nabhavo vidyate satah ubhayor api drsto 'ntas tv anayos tattva-darsibhih
Meaning: Those who are seers of the truth have concluded that of the nonexistent there is no endurance, and of the existent there is no
cessation. This seers have concluded by studying the nature of both.
When we consider our senses for confirming beingness many problems occur.
For a better understanding, (instead of tree) let's consider water for instance.
When we consider the three states of water we will have to consider three types of beingness (with slight variations). I mean, we will be compelled to treat/intoduce beingness as 'hard/condensed beingness', 'flowing beingness', 'divided beingness' etc. When we think about the water in the atmosphere, in/on the earth, in our body, in plants etc. we would certainly be in dilemma because this leads us to a folly--"a beingness in another beingness". In other words, a beingness made up of another beingness--Beingness having two types of 'qualities'. This is certainly nonsense.
I shall give more explanation:
When we consider a living tree and a dry tree we will be compelled to treat in two ways -- low-quality beingness and high-quality beingness (with out any separating boundary/criteria). This means, when we use this word we are treating some other quality or different aspects or something else; never as a separate 'being'.
The question is now whether these 'beings' are valid or not.
Since we cannot consider different types of beingness, this is invalid in this name.
Is there a real being what prohibit the other beings?
We would be in confusion if we think that real beingness is a part or the totality of sensual perception. So we should discard this attitude first.
There is only one beingness; I mean, what you meant as being must be the immutable all-prevading beingness. Actually this real being does not prohibit anything because there is no chance of another being (as you mentioned here). I have clarified it already.
Now you might have understood that the problem became complex because of the usage 'being'. If you had omitted that word you could have avoided the confusion.
Now your main question:
Is it possible to maintain the truth of levels of 'being'?
The consciousness that coordinates and make all of us feel this as a world (as by mass hypnotism), will maintain the truth of levels; but not as levels of being (See, I didn't use the term absolute truth). If you don't like the term--' mass hypnotism' you may say 'because of our ignorance'. But a coordination is certainly happening.
When you use the word 'being', the question becomes so precise that we can't say 'yes'.
I compared the thing, sense organs and the different views (you mentioned as different levels of truth) to white light, prism and spectrum behind it (respectively).
When you withdraw the white-light, the spectrum disappears. This implies, (just for comparison) white-light if it is taken as the real being, it can make the spectrum a mere nothingness. That means, here the spectrum has no separate beingness exempting the white-light. Therefore we can say that usage--'being' is in appropriate here.