I personally feel that the ones captured while in armed combat are in fact POWs. How can it be any other way?
Because of the Geneva Conventions. Specifically the 3rd one which states how prisoners of war are to be treated and how enemy combatants are to be identified. The problem in this war is virtually all prisoners are actually classified as illegal combatants since they don't fight for a particular country and don't wear a specific uniform to identify themselves with a specific country. (Taliban fighters might be an exception to this. I'm not sure if the Taliban actually wore standardized uniforms to identify themselves as part of the Afghan army or not.)
Imo, this whole issue isn't whether or not these folks are entitled to the rights granted by Habeas Corpus but what exactly is their legal status. Once their legal status is determined, then it would have been obvious what rights they did and did not have. Using the example from earlier in this thread, German PoW's didn't have access to Habeas Corpus and our civil courts. These folks in Gitmo shouldn't have access either if they are classed as PoW's or enemy combatants, legal or illegal. That precedent was set in Johnson vs Eisentrager.
Otoh, if some of those folks being held in Gitmo are being held as criminals, then yes, they should have access to Habeas Corpus and our civil courts.