It seems like the one thing that most people fail to take into consideration when considering such perplexities is the ability which God has to accomplish the unimaginable. What is really so unthinkable about the idea that they got on the Ark simply by God having literally picked them up and transported them there.
On that basis answering Moxy's question is sinch.
How could all the world's highest mountain ranges have been built up in the last few thousand years while providing all the evidence to the contrary?
Because, God made the mountains grow high very quickly while preserving the look of antiquity.
Why do lake varves and ice core samples show no evidence of the Deluge?
Because God created the mile thick ice sheets that only look like the oldest layers are 400,000 tears old.
How can bristlecone pines and other trees show continuous growth through the period to which the Flood is attributed with no signs of spectacular climate changes?
Because God picked them up and preserved them separate to the ark.
How did any flora survive underwater for a year, without sunlight, under fantastic pressures? How did such a devastating blow to worldwide ecosystems not leave geological evidence?
Same reason as previous
How did marine life survive? Different flora and fauna are suited to saltwater, freshwater, coastal areas or deep seas.
Same reason again
Most require sunlight and clean water. How could the turbulent mixing of water and debris not kill off entire ecosystems?
See previous
Why do genetic trees built with genetic biology not show a severe genetic bottleneck so recently?
Because God saved all the diversity separate to the Ark.
Why do so many sites like Egypt, China, Sumer, Indus, America show evidence of continuous human occupation through the time of the Flood?
God preserved human habitats so it only seems that there was continuous occupation.
How did the animals like the South American sloth and Antarctic penguin travel to the ark? How did they sustain themselves living in completely different environments? Why are there no traces of land bridges in geology and no traces of animals indigenous to these other continents in the Middle East?
Answered already
How did they travel back? How did they get off the mountain? How could the same land bridges have arisen after the flood?
God beamed them back Star Trek style
How could a water canopy contain enough water to flood the earth without raising temperature and air pressure to beyond that which could sustain life?
Water canopy didn’t exist, God guided dirty-snowball comets to create the flood.
How could such a large wooden structure have withstood the structural stress of the seas without leaking?
God put a protective force field around it.
How could delicate and evidently ancient structures like the cinder cones at Auvergne or the Great Coral Reef have survived the deluge?
God protected them with special force field enclosed air or water bubbles.
If humanity lived in a small enough area that Noah could have preached to everyone, then why flood the whole planet?
Because God can do anything, didn't you know that, silly?
Thirdson
'To avoid criticism, say nothing, do nothing, be nothing'