Well that is all Creationists really ever have - and you don't even have THAT!
Some OTHER mechanism? What is wrong with mutation and selection as a mechanism? Random mutation doesn't mean “beyond the control of God”, God's power doesn't stop at the casino door.
DNA replication is imperfect - as such just existing will introduce mutations into any population - and such mutational variations are then subject to selection - selection which tends to either increase or decrease the presence of that variation within the population.
What is going to STOP a 2% difference in genetic DNA from accumulating in different populations kept separate for a few million years?
Every species we see on Earth today couldn't POSSIBLY fit on the Ark - unless they were put there and kept there by magical means. Most creationists are of the opinion that there were only the primordial “kinds” of animals on the Ark - and they gave rise to all the different species - with each “kind” reproducing different species of the same “kind”.
'Evolution' is based on multiple logical fallacies invoked when convenient.
This one is known as the negative proof fallacy.
It is not logic nor is it an argument.
I don't think you know as much about creationist writings as even I do about darwinist writings. Numerous analyses using standard taxonomies have been done on this. Where is yours?