This has actually been observed; or is it speculation?
http://www.americanscientist.org/template/IssueTOC/issue/346
The first article discusses the speciation. The link below, (although long, sorry!) is a reprint. There is ample evidence to support the common ancestor theory; although I am sure that since the process took a while, you will deny that it happened, since no humans "observed" it.
http://chiron.valdosta.edu/jbpascar/Courses/Biol1010/ExtraCreditActivities/American%20Scientist%20Online%20-%20Adaptive%20Radiation%20of%20Darwin's%20Finches.htm
You YE-ers need to have a convention, get together, and decide what you really believe. It's difficult to have a conversation with a creationist without first going over the ground rules--speciation or not? 6000 years or 20000? Genome information addition allowed or forbidden?
The majority of YE creationists believe that speciation has occurred, so they would accept common ancestry for the finches on this island.