Chaunceygardner, there are much bigger and more obvious problems with your view. For starters, let’s start here:
“First, if we accept that God is infinite, then everything is contained in Him and He is in everything.”
That clearly doesn’t follow, even on a charitable reading of ‘infinite’ as a property. Take an example from William Lane Craig who notes that you could have a set of bricks, one connected to another, stretching infinitely in either direction (or indeed, stretching infinitely in one direction with a beginning end, it won’t make any difference). If the set of bricks is infinite does that mean that there is no x such that x is not part of the set of bricks? No, of course not; we can easily imagine a set of ducks next to the infinite set of bricks (whether the set of ducks is infinite in both directions, infinite in only one direction, or else just a set of three ducks in a row). Moreover, suppose that instead of a line of bricks you had a wall of bricks which was infinitely tall, so that it stretched infinitely in every direction (up/down and right/left). Would it follow that something cannot be next to the wall, like, say, another wall, whether infinite or finite? No, it wouldn’t follow.
The first problem, then, is that you misunderstand the implications of saying something is infinite. After all, the set of numbers is infinite, but clearly that doesn’t mean that there is no x such that x is not a number. Indeed, you might have infinite sets of numbers which do not include various numbers. For example, imagine the set of natural even numbers from 0 to infinity; that set is clearly infinite, but it also fails to include 1,3,5, … and in fact, for any n it does include, it will fail to include n-1. So, the set of values it fails to include is itself infinite (thus something’s being infinite even within a certain universe of discourse can fail to cover the whole universe of discourse, and can even leave an infinite amount of it out).
The second problem has to do with the way you seem to be attributing infinity to God, as though the infinite were itself some superlative attribute. It isn’t. To say that God is infinite is either a qualitative or a quantitative statement. If quantitative, then he is comprised of an infinite number of parts, and therefore isn’t metaphysically simple, from which a great deal of pernicious implications would follow. If the statement is qualitative, then we must ask how it qualifies. There is only one sense in which it could qualify God, however, and this is not by acting as some property on it’s own (for as a quality simpliciter predicating the infinite is vacuous), but by acting to qualify the way in which God has the various properties he does. Thus, for every great making property, God both has it, and has it infinitely (which is to say, without limit). God’s being infinite in this qualitative sense certainly doesn’t imply that for every x, if x exists then it is part of God. That reading is a quantitative one, not a qualitative one, and moreover it’s problematic, as I’ve shown, even on a quantitative reading.
“Third, you can neither gain nor lose your soul, since it is a part of God and is therefore eternal. It existed before we were created, and will exist after our physical bodies are gone.”
The trouble here is that you are acting as though the soul is something you ‘have’ rather than that by which you have an identity. The soul is not something you have, it is more accurate to say that your soul is what you are. You have a hand, you do not have a soul, for a hand is something ‘you’ can lose, but a soul is you yourself. If you reject that the soul is identical to the self (so that ‘soul’ and ‘self’ are interchangeable) then you’re in as bad a position as the materialist is in. How can you explain identity over time? If you say that identity is based on one’s physical parts then the integrity of one’s identity is compromised every moment of every day. If you say that identity is based on one’s psychological continuity then it is literally impossible for a person to get amnesia, since amnesia (or other conditions whose symptoms include psychological discontinuity) would just be the death of one person. If you say identity is based on mereological considerations, such as how the parts of your body are organized into a whole by a particular logic (DNA), then it would follow both that a person is their DNA (which hasn’t the ability to be conscious) and that a clone of that person would literally be that same person extended elsewhere in space. Without the soul one just cannot be a realist about persons at all, and thus I locate another serious difficulty here.