The apostrophe-M'hoon-was probably an attempt by some to show that a letter or letters were left out of the name.
Check
http://tinyurl.com/3l7dp and you will see two named Robert Mohoon in Cornwall / Devonshire. I got the record details from HeritageQuest. The other one I'm trying to tie in or eliminate is HEZEKIAH MOHOON shown in Martin County NC census of 1790. Were you able to get any further with this link
http://tinyurl.com/3l7dp and Revolutionary War?
Still a tangled web, but maybe we can untangle it...
BTW Verona, I understand you also met my sister Mary Kendall Maginnis from Baton Rouge.
NJOY.
Bob