[rrrrrrrrrrrryan]

Just dug a little deeper, and I've arrived at this conclusion:

In accents with the merger, "four," "for," and "fore" are all always homophones.

In accents without the merger, "four" and "for" are never homophones.

And in some subset of these non-merged accents, "fore" may be pronounced identically to "four" (as listed in the IPA guide in your first link). In another subset, it may be pronounced identically to "for" (as implied by the "Homophones" section in that same link).