A maximally great being is not burdened by too many relationships or having to balance relationships and the universe. This reflects a misunderstanding of the concept of being maximally great. A maximally great being is not burdened by anything as this would indicate a deficiency of greatness.
Honestly, your definition of "maximal greatness" incorporates wishful thinking. In effect, what you're really saying here is that because you've defined maximal greatness that way, that it must be that way in order to be maximally great. This is nothing more than a philosophical mind-trap; reality does not care about how you define maximal greatness. It does not matter what you include in a definition; what matters is whether that definition is a useful description for some part or another of reality. In other words, it doesn't do any good to say that your "maximally great" being has unlimited time and resources to pursue relationships unless you can show that it is possible to have unlimited time and resources to pursue other things.
But even leaving that aside, there's another problem with your position which I doubt you've considered. Say that your maximally great being really can maintain as many relationships as it needs to, that it does not need to balance them, and that it effectively has unlimited time with which to do so. The fact remains that none of those apply to humans, which creates at least two major problems. First, if time is meaningless to this entity, that means that no amount of time it puts into this so-called 'relationship' is worth the strictly finite time that a human has available to put into it. It doesn't even come close.
Second, these relationships are really so important, then the entity with more resources available to put into them has a greater responsibility to than one which has less. This should pretty much go without saying, yet for many Christians, especially Protestant Christians, it not only doesn't get said, but they somehow manage to get it completely backwards. If these relationships are so important to this entity, then it should be the one to pursue them. And yet, that is never the case. It's always up to humans to pursue a relationship with this entity.
Belief is not required to accept this premise. Even atheists can assent to the idea that the God conveyed in Christianity is a maximally great being which is the widely accepted view. Whether he exists or not is irrelevant to this premise.
Incorrect; if this entity does not really exist, then it cannot be maximally great. An entity that exists in the real world is necessarily greater than an otherwise-identical entity which does not exist in the real world. Therefore, your premise cannot be accepted unless a person believes that the Christian god actually exists. As not all humans believe this, this premise is not acceptable as part of an ontological argument.
I have addressed the concerns so the argument still holds.
And I have rebutted both again. I'm sure that you'll come up with answers to those, at which point I'll come up with additional rebuttals, until one or both of us is sick of it. This is why you need something more than logical arguments to prove a point.
Even leaving that aside, the fact remains that unless the Christian god actually exists, premise 3 is totally moot - because premise 2 cannot be true unless the Christian god actually exists.
If premises 1 through 3 hold, then this follows logically. Since I have addressed your arguments against the previous premises and no new arguments are presented here, it still holds.
First off, there is no reason to expect that the earlier premises will actually hold true. And in actual point of fact, there are very good reasons to expect that they will not hold true. For example, your first premise amounts to wishful thinking and special pleading - declaring that this entity of yours can ignore the limitations of the universe we live in for no good reason other than that it needs to be able to for your argument to hold true, as just one example.
Second, your responses to my arguments were far less than satisfactory. In effect, they amounted to you arbitrarily declaring that my arguments didn't apply to yours and thus that your arguments therefore remained sound. This is a useless way to argue, because you aren't going to succeed in convincing anyone that your arguments are, in fact, sound; what you are much more likely to do is convince people that you won't take objections to your arguments seriously.
You seem to miss the word "if" in the premises. This has not been an argument for God's existence, but rather, what we might expect if God exists. If the first two premises hold, the final three are the necessary logical progression. Unless there are further challenges to premises 1 or 2, this argument still holds.
I did not miss your conditional statement. The problem is that the Christian god must actually exist for this to be at all relevant. Even if it does exist, it might not be a maximally great being, in which case your argument would not apply to it; you are simply assuming that it is maximally great, without any basis in fact. Anyone can imagine a theoretical "maximally great" being without that being actually existing in any way, shape, or form.
And finally, there is no reason to presume that the world could not be better than it is. Even if an entity was maximally great, that does not mean that it would have to have put forth its best possible effort. An entity which can only put forth its maximum possible effort is inferior to an identical entity which can put forth less than its maximum possible effort, provided that it can choose the amount of effort it puts forth. And you are ignoring the actual limiting factor, intelligent beings, which even a maximally great being must cope with. A chain is only as strong as its weakest link, so even if you had a maximally great being around, it would still be limited by what intelligent beings in this universe could do. Therefore, even its maximal greatness would be stymied overall by the far less than maximal qualities of ordinary human beings.