EDIT: I have been told that what is obvious to me may not be obvious to others. I assumed that it was obvious that I believe Romans 1 to provide context for 1 Cor 6 due to my repeated quoting of them together in the OP and elsewhere. The argument that malakoi is unclear (and therefore not applicable to homosexuality in any way) is supported by a parallel appeal to the ambiguity of Romans 1. However, we have a wonderful example in Plutarch where he uses both terms together to refer unquestionably to homosexuality.
Obviously, I'm running up against the fact that I do not read Greek, either modern or Biblical, but I do realize that words can have different meanings depending on context.
You've stated that when a man is described as both "soft" and "contrary to nature", that this usage of the two terms indicates that it's intended to describe the man as homosexual... fine. I don't see why that this means that every instance of the word "soft" without "contrary to nature" implies that the person is homosexual, especially when we can see that similar terms in modern English can convey a meaning of "unmanly" or "effeminate" without implying that the man in question is gay.
As an example: a person may be described as "green with envy". This does not mean that another instance of someone else being described as "green" automatically implies envy, because there are lots of other meanings (e.g. sickness, inexperience, etc.) that the word "green" can denote.
In the case of 1 Corinthians 6, we have, as I see, it two possibilities for the intended definition of
malakoi: homosexual men, or men overly focused on earthly comfort. The latter possiblity definitely fits into the teachings of Paul as a whole (he isn't too big on "the flesh", after all), so I don't see why it should be immediately discounted.