Eunice,
There were 2 female slaves freed in 1798 named Eliza & Nancy HART, but I couldn't tell you anything else about them other than that.
In researching your Captain HART, have you taken into consideration that there was a middle name somewhere in there? I have several people in my tree who had first names like "Captain, Major, General, Governor, Lieutenant, etc.", and it turned out their names were like "Captain John Smith _____(insert surname)", "Major Lewis ____", "Governor Ellis _____", "Lieutenant Boyd ____", "General Andrew Jackson ______", etc. Our ancestors were quite fond of naming their children after known figures of the time.
Also, as I have said in another thread on this Forum, it really wasn't unusual for a former slave to use different names in the census, sometimes they seem to have tried out a few before finally settling on one. You may want to check for records in the US Colored Troops, too, quite a few former slaves enlisted in one state and ended up in another by the time of the census.

Deloris