No, you can't. You can link how 'of' can be used to construct a nonsensical phrase all day long. It's still nonsensical. That being said, learn the language. 'Conscientious of' is an acceptable usage in a stubborn imaginary world in which usage is subordinate to your preference.
At this point, I think this thread has gone way too far of course, but I'll give clarification one more attempt.
I think the confusion here is in neglecting the various definitions of the word, "conscientious," in combination with the aforementioned definition of the word, "of." In terms of being guided by conscience, or of being thorough and assiduous (two possible definitions), I agree that being "conscientious of" something makes absolutely no sense.
However, it can also mean to be careful (more along the lines of my intentions), in which case using "of" certainly makes sense, as you can be careful of some idea. Perhaps next time I comment, I'll just say "careful" to avoid the confusion.
Furthermore, it's important to remember that English is an ambiguous language. Part of the beauty (and perhaps the downside) of the language is that there are no rules, only guidelines (this is a good article on the subject: http://www.nytimes.com/2010/01/01/books/01book.html). The best we can do is to know our audience and tailor our language to most effectively communicate our message. If nothing else, this thread has at least taught me something of my audience (something I should have known: that we are all very detail-oriented and so care must be taken in our communication). Perhaps saying "conscientious of" was not the best and most effective use of the word, but to say it's "wrong" or unacceptable I think is quite naive.
