I know this is an old message that I am replying to and hopefully by now you have found your Moody's. This caught my eye because I too am searching for my own MOODY family in/of the Limavady area.
The link you showed in your message from Lesley MOODY with the ALEXANDER's is of interest to me because our Ydna MOODY's also have a link to the Alexander's.
Just a bit of background...our earliest known Moody ancestor was a Thomas MOODY b.c1710 in/of the Aghadowey area possibly being from Limavady though.
He married Jean McQUISTON daughter of Benjamin and they and several other families came to New Castle, DE in c1735.
They removed to PA briefly and then went further south to Guilford Co., NC (lots of info on line about them).
If anyone has further info regarding these MOODY families I would be Most interested.
The William MOODY (father of your Lesley) who married Jane ALEXANDER in 1798, do you happen to know if this William had a brother or a relative named John MOODY who owned a bleach green?
A William and his half brother Robert MOODY (both sons of a John Moody but they had different mothers) came to Pittsburgh, PA in the early 1800's. William married into the LEDLIE family and they had links to the EAKIN/EKIN family all coming out of Nor. Ireland to America and some I believe were from this same area where the Moody's were from...the Limavady area.
Thank you for any info at all.