Stump the Christian?

[dyresand]

No.  They can't be investigated let alone refuted.  You don't get to concoct unfalsifiable premises and then treat that as 'reasonable'.

Because you can't test them does not mean they are unfalsifiable. A statement is falsifiable if it is possible to conceive an observation or an argument which proves the statement in question to be false. You know they are not baseless--you are very familiar with the arguments. Again, you might not like the quality of the evidence or believe an alternate theory, but following the evidence we have is quite 'reasonable'. 

Science works with in the realms of reality not fantasy. A unfalsifiable claim would be pseudo science and pseudo science isn't science at all. 
It's like me claiming to make a scientific statement such as if you think about Orange Monkey Eagle at the same time your brain will shut down.

1. Pseudoscience is a claim, belief or practice which is incorrectly presented as scientific, but does not adhere to a valid scientific method, cannot be reliably tested, or otherwise lacks scientific status.
   

So you claim these things are unfalsifiable and they did happen you are just making incorrect statements that are in the realm of pseudo science and fantasy.