Tim,
All four of the philosophers are basing their position on a purely rational approach to our world, and the idea that "it is impossible for immutable laws to be violated." This is something that Christians simply do not accept. We have no problem at all with the supernatural, with God overruling His own laws. So, the miraculous is not an issue for those who accept the supernatural by Faith.
Now, turning to the science part. Where you are getting it wrong is confusing what science can investigate and comment upon on the one hand, and what science can "rule out". The fact that science can not investigate and make statements about things outside of natural laws does not, in any way, mean that they "rule it out".
Oh, I think I see where the problem is. You are also not distinguishing between naturalistic methodology and naturalistic philosophy (or philosophical naturalism).
Naturalistic methodology is simply the process of determining what happens within the natural world, not what may happen via supernatural forces. The "scientific method" uses naturalistic methodology to explain the natural order of things, how things happen in the absense of the supernatural. Science, using naturalistic methodologies, does not exclude the supernatural as a possible force, it is just not equipped to deal with it, and so doesn't try to.
Science is not the sole arbiter of truth about how the world works or what happened in the past, it is just a single tool to determine this. This tool is used to determine what the natural evidence says.
Naturalistic philosophy, on the other hand, is the belief that all must happen according to natural forces, and that any forces which can not fit within these natural forces should not be accepted or given any consideration as a possible causitive agent.
Former, good. Latter, bad.
All scientists, whether Christian or not, whether they accept the supernatural or not, use naturalistic methodologies. Scientists are in the business of explaining how things work in their natural state, so this is process they must use.
Now, many scientists are, indeed, not only using naturalistic methodologies, but have a naturalistic philosophy and, to the extent they let this philosophy show, they are no longer speaking as scientists, but simply espousing their philosophical underpinnings.
Scientists who are Christians use the naturalistic methodologies in every aspect of their scientific research, and rightly so. Their job is to discover all the natural processes which God established in this world. This is great, and not a threat to Christian belief in the least.
Now, when we review the evidence, we need to just make sure to weed out conclusions that are not based on the naturalistic methodologies alone, but which are influenced by naturalistic philosophy. This requires "rightly dividing the word of truth", just like we do with reviewing the preaching of word.
Accepting the conclusions reached by naturalistic methodologies is something we do every day. You accept that rainbows are created by light refraction, and are not just supernatural events. You accept that lightning is a natural process and not just a sign of God's anger. And, when the evidence about or past is soundly based on naturalistic methodology, and not naturalistic philosophy, it should be accepted to the extent it IS sound.
So, by this process, we get what the evidence from God's Creation is, and the conclusions drawn from that evidence are reliable to the extent it is supported by the evidence, and to the extent there was not a supernatural force or event which overrides that conclusion.
For example, we can say that the evidence from God's creation can lead us to the conclusion that no living being has been raised from the dead UNLESS there was a supernatural event. We, as Christians, believe that such supernatural events have taken place.
Now, here is the essential angle when it comes to the age of the earth, the flood, etc. The fact that we are willing to accept the supernatural, and must qualify our scientific conclusions with the possibility of the supernatural, there are times when we can know that a particular supernatural event did not occur. NOT because the event would violate a natural law, that is NEVER a reason to say an event could not occur (that is a very important point, and where the strawman comes in).
Instead, we can know a supernatural event did not take place when there is specific evidence present that WOULD NOT BE THERE had the supernatural event occured. OR, if a particular supernatural event did take place, it would leave specific evidence which is NOT present. If either one of those is true, then we can know that the particular supernatural event did not take place. Or, better to say that to the extent that the evidence is there that should not be there or that the evidence is not there that should be, we can conclude that the supernatural event did not take place.
Why? Because God is in charge of all that evidence, and would not leave behind evidence that could only be there if the event did not take place. And, He would not remove evidence that would necessarily be there if the event took place. I think you would agree that God is not the author of confusion and would not play tricks like that.
This the case with the flood, for example. There is a great deal of evidence which would not be there if a global flood took place within the last 10,000 years. There is also a lack of evidence that would be there if it had. These are all set out in great detail in many threads in the other forum, and this is not the place to go into all of that.
So, given this, I think it is much more likely that the text was not referring to a literal global flood.