i am sure someone has addressed this but i will give it a go:
"But the soils at 4,350 years ago don't contain evidence of a global flood."
it is better for you to say: 'the soils i assume to be 4,500 years old and studied do not showe any flood evidence"
you and i both know that studying samples is a limited way to go about discoverying evidence. one reason you did not see any evidence is that you picked the wrong soil, whether by age or location.
another is construction or wars, earthquakes, and subsequent floods destroyed the evidence you are seeking.
remember that wooley went down about 90 feet or so and found virgin land and called it flood level,{ he was forced to recant later}, so you may have gone to the wrong depth. finding 10,000 or 4,500 year old dirt is not that easy as its depths are not uniform and dating is too subjective.
also, you are assuming that Noah's flood acted like a local river uprising, we cannot be sure how it acted since not all of the water disappeared and the geography was changed and was not the same as the pre-flood lands.
then you have to consider regrowth of plant life, rivers changing courses and so much more. it is said that there was a huge lake in the area if the modern sahara so what kind of erosin are you going to look for in the sand and froma lake drying up?
just some ideas for you to think about.