You are trying to have it both ways. By saying that the long time periods are acceptable, then yu are saying that on one day of creation, as listed in Scripture, that we had plants for eons of time before we had a Sun.
First of all, so what if I am? Plants could not survive for one instant on their own without the Sun. So if they were created before the Sun, it would take a continuous, sustaining miracle of God in order to keep them alive. God could easily keep them alive for millions of years as one day, it makes no difference to Him.
However, I don't actually believe that the Sun was created before the plants. Ah, yes, I am a heretic, aren't I? No, not at all. I still believe that Genesis 1 does give an accurate order of events. But how is that possible, then? You are right, it seems as if Genesis 1 is saying that the Sun was not created until after the plants.
The key is this: Genesis 1 is written from the perspective of the surface of the Earth. Remember, the Spirit of God was "hovering over the waters" Earth! So if you were sitting on a lawn chair on the surface of the earth (presumably it would have to float on the water :), then you would see exactly what the Spirit of God was "seeing" during Creation.
To make a long story short: the sun and the stars were already there from Day 1. However, the Earth's atmosphere was changing. Before Day 1, the atmosphere was opaque, which means that no light from the stars, sun, and moon could make it down to the surface of the earth. Then, on Day 1, God said, "let there be light", and he made the atmosphere translucent. This indeed brought light to the surface of the earth---day and night---but it was not yet identifiable as the sun, moon, and stars. This light was sufficient to support the plants that he was creating on Day 3. Then, on Day 4, he made the atmosphere transparent, as it is today---thus revealing the specific structure of the sun, moon, and stars. From the surface of the earth, it would look exactly as Genesis 1 described: as if the light was coalescing together into the sun, moon, and stars.
So you see, I do not give up the order of events in Genesis 1 at all. No compromise in Scripture needed. If you're actually interested in learning about progressive creation models instead of ranting against them (or flat-out ignoring them in your arguments), then you might consider reading some of the resources written by Hugh Ross and the Reasons to Believe foundation (http://www.reasons.org). New advancements in science continue to validate the accuracy of Scripture every day.
I know you will probably consider progressive creation heretical, even after you actually learn what it is. But perhaps you will at least learn to concede that people who fervently believe in the truth of Scripture can disagree with you as to its proper interpretation, and fervently believe in a version of creation that is not 144 hours long.
You are free to have the last word on this. But if you're just going to repeat that I don't believe in Scripture, don't bother. You've already said it.