While reverse coding 1->10, 2->9, 3->8, 4->7, 5-> 6, 6->5.. so on. The issue is that the neutral point 5 becomes 6, which will be contradicting already collected data with positively worded survey questions. Any suggestions?
If you want a true midpoint, you need an odd number of items in your scale. What you are saying is that 5 isn't a true midpoint, so you are trying to replicate something that never existed in the first place. Just proceed with the recoding you mentioned, recognizing that 5 and 6 collectively represent the closest one can come to a midpoint.
If you already have data, which it reads as though you do, then you do not have a midpoint. You don't a have a "don't know," or a neutral value choice. If this is a survey research project, and you collected data from respondents based on a 10-point scale, you have a serious design flaw. You can't just go recode data to make it say what you want it to say. You will have, at a minimum, a serious validity problem: claiming data mean something they don't, or claiming respondents said something they did not.
I think you have two choices. First, admit you designed a faulty survey instrument and use the data as you collected them. Second, go back to your respondents with a 5 or 7-point scale and redo the study.
If you don't know anything about research design, perhaps find a partner who does. You pretested the survey, correct? If you didn't pretest the instrument, then you have serious threats to validity regardless of the problems with data collection and coding. For reporting, either admit all your flaws and weaknesses up front, and go with what you have. Or do it over.
In itself, there is nothing wrong with a 10-point scale, though it is probably more categories than people naturally use. There is also nothing wrong with reverse coding when one item is phrased in a negative manner. I suggest that you first look at the distribution of responses; it may be that the responses are largely clumped on one side or another, and that the midpoint is largely irrelevant. True neutrality is hard to measure; the more categories you offer, the fewer responses will fall in the middle.