The 1901 Irish census has 86 McCormick/McCormacks in Co. Armagh. So you need to be careful that you find the right family. Not all parishes have records for the 1830s so it’s easy to seize on the wrong record on the basis that, since it’s the only apparent match, this must be it.
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project in conjunction with Family Tree DNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website). You don’t need to be a member of the NIFHS to participate in the DNA project.