If I'm not mistaken, I see an additional problem for theism in your solution to the first time problem. Traditional theism, I think, asserts that God is prior to everything else.
In the beginning was the Word, and the Word was with God, and the Word was God.
Given the above quote, I'm skeptical about traditional theism accepting that time is co-eternal with God (even if God says so!) — ucarr
Forgive my ignorance, but I cannot reply to your comments about set theory, as I do not have any meaningful understanding of set theory. However, I did follow this above quote and I believe you are providing me with two arguments. The first one looks like this:
1. On traditional theism, God is prior to everything, including time.
2. If God has willed that time always exists, then God is not prior to everything, namely time.
3. Therefore, traditional theists cannot coherently say that God has willed that time always exists (1, 2).
I think this argument commits the fallacy of equivocation. In premise 1, traditional theists are committed to say that God is
ontologically prior to everything. In premise 2, God is not
temporally prior to everything. Thus, you seem to be equivocating two uses of the word "prior." To help illustrate this distinction, consider the example of the relationship between fire and smoke. Fire is ontologically prior to smoke. In other words, smoke is ontologically dependent on fire. If there is not a fire, then there is no smoke. However, fire is not temporally prior to smoke. Once there is fire, then there is instantly smoke. They come about at the same time. Thus, fire is ontologically prior to smoke, but not temporally prior to smoke. Similarly, God is ontologically prior to time (as it is willed into existence by God), but God is not temporally prior to time. Further, God cannot be temporally prior to time when there is no temporality to begin with. For these reasons, I do not think this argument works.
As to your argument about the Word existing with God, this does not seem to be an issue with Christian theists. Christian theists affirm that the Word is of the exact same identical nature as God. Thus, there is not issue with ontological priority. On this view, there are not two Gods who both have ontological priority, but rather one God. On Christian theism, the Trinity is three distinct persons who all share the same nature, which is God. In the same way, you and I can share the same nature---human nature---but can be distinct persons from one another. I hope this helps clarify the discussion!