"More perfect" versus "less imperfect"
Solution 1:
The paradox: "more perfect" and "less imperfect" should mean the same thing, no?
I wouldn't say that's a paradox. To my intuition, "perfect" denotes the extreme point in a continuum. Everything else in that continuum is thus "imperfect". Therefore, "more perfect" makes no sense to me, as you point out. But "less imperfect" does.
However, I have learnt that "perfect" is used in comparisons in everyday language. I am aware that some reputed dictionaries and linguists are against prescriptive advice, but since this is a Q&A site, I'd rather position myself and give positive advice. Fowler's reads on this matter:
in most circumstances perfect is used as an absolute adjective, but there are somewhat rare occasions when the speaker has in mind a near approach to such a state and a comparative adj. or the adverb very may be appropriately used with it.
In conclusion, I would try to avoid to use "perfect" in a comparison, with the only exceptions of metaphorical or approximate usages of the underlying concept of perfection.
Solution 2:
Many of the senses of perfect are comparable, so there is no reason to presume that more perfect is somehow “bad English”. The many examples of that usage, even in very formal writings, such as the U.S. Constitution, should be sufficient proof of that. Frankly, the idea that you could use a “logical” argument to declare some usage “bad English” is in itself fallacious. It is easy to forget that most words have multiple meanings and can be used in more than one way. On a related note, the same is true of unique.