Doing the math
Look, I'm not here to chastise you for your beliefs, but there are about 5,000 species of mammals alone on planet earth. That would mean that over 10,000 mammals were on board. That excludes insects, reptiles, invertebrates and birds.
Secondly, all but the heartiest and atypical plant life on earth would have died after being submerged in salt water for a such a period. Where did Noah put the over 250,000 species of currently identified plants?
And what about freshwater fish? A sea level of 17,000 feet would certainly mean the waters of the Biblical flood would have been saline, making life impossible for freshwater fish. Thus, by biological necessity, Noah would have had to accommodate for the 12,000 species of currently identified freshwater fish.
Or, conversely, the waters may have been non-saline, meaning that Noah would have had to contain over 14,000 species of saltwater fish.
That would mean, realistically, that an arc of the proportions you've mentioned, would have been completely full of water to contain so many species.
Either you have your measurements incorrect, or...