There is nothing on any of the names for Welch or Elliot, however, if those were the individuals surnames that you have for them in later years, please note that most slaves didn't have surnames listed in their emancipation records. And many slaves did not necessarily take the surnames from their former slave masters, either, so it's best to seek slave info under the slaveowners name. However, at least 2 of the names you gave are unique enough for me to have checked the slave index by first names and I have come up with some possibilities. The dates for these records are close enough together for there to have possibly been a connection at some point.
You don't mention any dates, but the name "Annice" comes up in records filed in Perquimans County,NC in regards to a female slave named "Annis" who had formerly lived in Edenton, Chowan Co.NC:

PERQUIMANS COUNTY RECORDS
Harrison Douglas,
Petition for Emancipation , April Term 1825
Extended in the Minutes

State of North Carolina Supreme Court of Law, Perquimans Co. Ss April Term 1825

To the Honorable the Judge of the Superior Court of Law for the County aforesaid The Petition of Harrison Douglas a free person of Colour of Perquimans County humbly sheweth
That he hat lately intermarried with a negro girl slave named ANNIS, who at the time of such marriage was the property of Elizabeth L. Blair of Edenton - that since the marriage the said Elizabeth in consideration of the excellent character & former services of the said slave has given to your Petitioner a Deed of Gift for the said girl ANNIS & with a hope that she might be liberated - Your Petitioner sheweth that the said girl ANNIS has always supported an irreproachable character, has been remarkable for her moral & correct behaviour & industrious habits -- He therefore prays your Honor that he may be permitted to emancipate the said slave & as in Duty bound he will ever pray &C.

JA IREDELL
Atto. for H. DOUGLAS

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(Copy of Petition)

On hearing the forgoing Petiton of Harrison Douglas & testimony in support of it It is considered & so adjudged by the Court that the said Harrison Douglas have permission to emancipate the said Woman ANNIS upon his entering into Bon as the Act of Assembly requires - Whereupon the said Harrison Douglas entered into Bond as required by Law with Edward Wood & James Iredell as his securities which is approved by the Court -- and it is permitted to emancipate the said woman ANNIS.
To be put on the minutes and a copy del'd Harrison with the Clks seal & Certificate

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Harrison Douglas
Emancipation Bond
April Supr. Court 1825

State of North Carolina Ss.
Know all men by these presents that we Harrison Douglass, Edward Wood and James Iredell are held and firmly bound unto John Clary Chairman of the Court of Pleas and Quarter Sessions for the County of Perquimans in the sum of one hundred pounds to be paid to the said Chairman & his successors in Office for the use of the Poor of the said County, to which payment well & truly to be made we bind ourselves, our & each of our Heirs Executors & administrators firmly by these presents. Sealed with our Seals and dated this 21st day of April 1825.
The Condition of the above obligation is such that whereas the said Harrison Douglass hath been by the Superior Court of Law for the County of Perquimans at the present Term thereof permitted to emancipate a negro woman by the name of ANNIS, now if the said woman ANNIS after being emancipated in pursuance of the said permission shall never become chargeable to the said County of Perquimans or to the Wardens of the Poor thereof, then the above obligation to be void - otherwise to be full force and effect.
Sealed & Delivered
HARRISON DOUGLASS
JAS IREDELL
EDW. WOODS

In presence of
FRANCIS TOMS

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There was also an entry for the name of "Nelson" in Craven County,NC, for which I don't know if this is yours, but perhaps it will help:

State of North Carolina
Craven County

Know all men by these presents that We Donnum Montford are held and firmly bound unto his Excellency James Iredell Esquire, Captain General, Governor, and Commander in Chief of the State aforesaid, in the full sum of two hundred pounds, to be paid to the said Governor or his successors i office; to the which payment well and truly to be made, we bind ourselves, our heirs, executors, and administrators, jointly and severally, firmly by these presents, sealed with our seals, and dated this 29th day of February A.D. 1828.
The Conditions of the above obligation is such, that whereas at the Court held for Craven County, at this day permission has been granted to Donnum Montford by the said Court, to emancipate and set free a certain negro slave named NELSON. Now if the said negro so permitted to be liberated shall during his residence in the State of North Carolina behave [Blank] as an honest and peaceable citizen, then the above obligation to be void.

DONNUM MONTFORD

Sealed and delivered in presence of
JNO. STEWART STANLY

----------------------------------
State of North Carolina
Craven County

Know all men by these presents that we Donnum Montford are held and firmly bound to John F. Smith Esquire Chairman of Craven County Court, in the sum of one hundred pounds, to be paid to the said John F. Smith or his successors in office, to which payment well and truly to be made we bind ourselves, our heirs, executors, and administrators, firmly by these presents sealed with our seals and dated this 29th day of February 1828.
The Condition of the above obligation is such, whereas at the Court held for Craven County, at this day permission has been granted to Donnum Montford by the said Court, to emancipate and set free a certain negro slave named NELSON. Now if the said negro so permitted to be liberated, shall not become chargeable to the parish of Craven County, or of any other County in this State, then the above obligation to be void.

DONNUM MONTFORD

Sealed and delivered in presence of
JNO STEWART STANLY