I am looking for a way to replace the word "being" in the phrase "being of poor character". My instructor is very adamant that we not use being unless it is used as a noun. In this particular case, I am having trouble replacing it.
That's because your instructor is wrong. You definitely need a new instructor. That sentence is absolutely fine.
He, being of poor character and strong rashness, insulted some gang members and was beaten up.
Your instructor is wrong, of course, but I understand what he or she is trying to do. Often being, is used in a participle phrase when a stronger two-clause construction sounds better. Being late, he missed the bus. Because he was late, he missed the bus. On the other hand, sometimes you need being as part of the verb-phrase. Which of the following best describe an individual who over-simplfies are rule of grammar. The first one: He is being lazy. (Note the implied reference to some activity or action.) Or, the second one: He is lazy.
Well I agree, your instructor probably isn't the best, but right now let us just look at a workable alternative to being.
As he was of poor character,...