The Minecraft model of the Trinity

As a person, I can take more than one form! I have my normal bodily form – that is, I am made of flesh and blood, just like all humans are. But when I play Minecraft (a computer game involving a simulated world) with my son, I am represented by an avatar (a computerised image of a person, that I control) by means of which I can walk around, build houses etc, in the virtual environment. In the Minecraft world, that avatar is, in a sense at least, me. My son will say things like, “you can come and visit me in my house”, and when he says “you” he is not referring to the flesh and blood me, but to my avatar. Likewise, if I decide to write a story and portray myself as one of the characters in the story, that character – even though he may get up to things that I’ve never actually done in real life – is also, in a sense, me. It's not merely that he is based on me; within the world depicted in my story, that character is me. The other characters in the story will refer to him, quite rightly, as Andrew (my name). So, in this sense, it is possible for me to exist as one person in at least three distinct forms.
Now, I realise that the doctrine of the Trinity is very different to this. God is not one person with three distinct forms. He is beyond mere personhood. So, whereas I can be one person in three distinct forms, God can be one Being in three distinct Persons. And whereas, in my case, each of the three 'objects' (flesh and blood, Minecraft avatar, story character) has the same one 'subject' (me), in the case of God, each of the three subjects (Father, Son and Spirit) has the same one superpersonal,divine Nature (God). But the two concepts (that of one person in three forms and that of one Being in three Persons) can be regarded as analogous. And this analogy can, it seems to me, clear up many of the apparent logical inconsistencies that have previously plagued my many attempts to understand the doctrine of the Trinity.
For example, in the above scenarios I described myself as one person in three forms. The flesh and blood me, is (obviously) me – in fact you could probably call it the only true me (and Jesus, in John 17:3, calls the Father "the only true God"); the Minecraft avatar is me; and the story character is me. Yet, even though I exist in three forms, not one of those forms of me has three forms itself. The flesh and blood me isn’t a Minecraft avatar or a story character, the Minecraft avatar isn’t flesh and blood or a character in a story, and the character in the story isn’t flesh and blood or a Minecraft avatar. Yet still, in some sense, each of them is me. You could say that while the Minecraft avatar (for example) is me, there is more to me than a Minecraft avatar.
If the ‘me’ character in the story that I’ve written gets bitten by a dog in that story, then it would be true to say that I have been bitten by a dog (in the story) while at the same time it would also be true to say that I have never been bitten by a dog (in real life). So, because of the existence of different forms of me (the flesh and blood, the Minecraft avatar and the story character) inhabiting different levels of reality (the real world, the Minecraft world and the story world) it becomes possible to say that I have been both bitten by a dog and never bitten by a dog, which sounds like a logical contradiction and yet is true because - even though there is only one me - that ‘me’ exists in three different forms.
Bearing all of the above in mind it becomes possible, by analogy, to say things like the following:

The Father is God, the Son is God, the Spirit is God; the Father is not the Son or Spirit, the Son is not the Father or Spirit, the Spirit is not the Father or Son – and yet there is only one God.

or,

God became a man and was crucified. The Father is God. The Father did not become a man or get crucified. There is only one God.

In the past I have considered these types of statements as being self-contradictory and therefore illogical and incoherent, but – if one remembers my description of one human being (me) in three forms, and the paradoxical-yet-true statements that can result from that concept – then it is possible, by analogy, to hold each part of the above statements as simultaneously true and not indicative of any contradiction.
In other words, if you accept that it is possible for a human person to exist – in some sense – in three forms, then you must also accept that it is possible for a Divine Being to exist – at least in some sense – in three Persons.