Since Edwards’/Calvin’s notion of God is not on this point any different than Arm or Kath notions of God (whether Protestant or Catholic), then obviously this is not what non-Calvs are complaining about, duh.
It is however normal for Calvs to sidestep what is actually being complained about in the charge of egotism, and to pretend that they’re only saying what everyone else already agrees with (thus they either act confused about why anyone would complain about what everyone already agrees with, or they counter-charge non-Calvs with not believing what everyone already agrees with.)
The problem comes in when Calvs try to appeal to this as an explanation for God choosing to ensure ultimate injustice happens by creating and supporting creatures which by God’s authoritative choice God never even intends to empower and lead to do righteousness, who thus can only do unrighteousness.
Since that would normally be regarded the height of injustice, Calvs attempt to explain this as being instead so that God can be sure someone exists for Him to oppose with His justice. And so they have God acting utterly and fundamentally against the well-being of other persons in order to promote Himself in some fashion. That this promotion is totally useless to God, since God has no (or should have no) need to bloody his sword to make his justice shine brighter (so to speak) in his own estimation, only makes the explanation worse; since now God is creating creatures to torment and kill forever in order to impress other creatures who, on this theory, would not be able to properly appreciate the glory of God without other creatures being sacrificed by God to hell.
None of which is good psychology, incidentally. Though it does fit the observation that “People always try to bring God down on their level”: creating the worst possible unending injustice is what some people think of as justice, so that’s what they think they need to see God doing in order to appreciate Him better. So, they use that as an explanation for why (they think) God intentionally chooses not to save some sinners from sin even though they realize He could successfully save all sinners from sin if He ever intended to do so.
The problem isn’t the egotism of God. It’s the dangerous egotism of the people who come up with this particular theory which they’re projecting onto God: this is what they would do to other people to make themselves feel they have more self-worth.
But God has no self-worth problems prompting Him to sacrifice creatures, much less any rational creatures whom He gives rational spirits, for the sake of His own glory. On the contrary, God sacrifices Himself for the sake of all creatures (and even for all creatures to exist at all): the trinitarian God is totally self-giving.
Any punishment dealt out by God must thus be consonant with God’s own intrinsic trinitarian reality of justice fulfilling love.
Or putting it another way, Jesus’ way (GosJohn 5:19-30): the purpose of the judgment by the Son, and the Son’s resurrection of those who still do evil things into eonian crisis, is so that all may honor the Son even as they honor the Father, with a term for ‘honor’ that means to positively and properly value. Those who do thus honor the Son receive eonian life and come out of the death into life.
It is expressly on this principle, of rebels coming to properly honor the Father and the Son, that Christ declares His judgment is just. Any theory of judgment resulting in rational creatures never coming to properly honor God, must on Jesus’ own explicit terms involve attributing unjust judgment to God or an impotent failure of God’s judgment.
Putting yet another way: any theory where God refuses to lead those persons who don’t properly value God to properly value God, runs completely against what you’re saying (or copy-pasting from Calv sources) in your post here, Cole. God would be acting to make sure various rational creatures never can and never do properly recognize and value Him as the most glorious and greatest of all beings.
Only one version of punishment fits what you wrote: a punishment of persons already empowered by God to do justice, but who are themselves choosing not to do justice yet even though they could, with the successful goal of leading them to do justice instead – including to properly value God (which, insisting on injustice, they aren’t doing yet).
Anything less than that goal and that result, involves God voiding and acting finally against God’s own valuation of Himself. The Son would be choosing that some rational creatures never properly honor the Father; the Father would be choosing that some rational creatures never properly honor the Son. The Father and the Son would be choosing to permanently and finally dishonor each other, by the authoritative proxy of creatures finally dishonoring each other. Which, not-incidentally, would tend to involve the Father and the Son egotistically promoting themselves over-against one another.
It’s a great thing, then, that God truly is not egotistical. 
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