The will I transcribed of Nathaniel Heywood sounds very much like that of a bachelor, who is leaving bequests for this extended family and friends.
He is of Puddington, and the will was written on November 30th 1803, and proved on March 7th 1804.
As you point out, he does not mention his wife, (she could have been dead of course), or any children specifically.
The only direct relationship of his given is that of Elizabeth, his sister, married to George Mortimer.
The only marriage I could find between that of an Elizabeth Heywood and George Mortimer was 2.2.1751 at Exeter.
If this is the same people, she may have been born about 1730, so this Nathaniel may have been about the same age.
Unfortunately, there is no indication as to the age of Nathaniel Heywood in the will, or in the Puddington burial register entry on 3rd Dec 1803, just 3 days after he wrote his will.
There is also a Nathaniel Heywood buried 3rd Nov 1803 at Rackenford. Also no age given. This is presumably the Nathaniel Heywood of Rackenford mentioned in Nathaniel of Puddington's will. The marriage of Nathaniel in 1799 to Mary Moore, and the baptisms of Betty in 1800, and Mary in 1804, were all at Rackenford. Although the BAPTISM of Mary on 21st Feb 1804, is after the father was buried on 3rd of Dec 1803, it's entirely possible this is his child. Sometimes you see 'deceased' after the father's name, but not always. And although Mary was baptised in Feb 1804, she could have been born before Nathaniel of Puddington made his will on Nov 30th 1803. Or there may have been another child between Betty in 1800, and Mary in 1804. Have you checked this out?
I would say therefore that there were 2 Nathaniel Heywoods. One in Puddington, an unmarried bachelor, and another in Rackenford, the father of Mary and Betty. This one unfortunately does not seem to leave a will. He is given as a butcher on the marriage record.
One might suppose these two men to be related in some way - perhaps cousins, or uncle and nephew (it seems possible one is about 30 years older than the other), but you would need to go back to previous generations to check. I can only see one baptism for a Nathaniel Heywood - 12th Feb 1768 at Rackenford of William and Jane. That's not to say there might not have been another one, or he may have come from further afield than the small area around Tiverton.
There are lots of names in this will to do some research on.
I have spent some time, but you need to look at a variety of sites. Not all Devon records seem to be on any one site. Familysearch have some, as do findmypast. Pcc wills are on ancestry, and The National Archives Discovery site is always a good place to search for records that might be there or at County Archives.
George Maunder married a Mary Heywood 22 Sept 1798 at Cruwys Morchard, where she is given as being of Puddington and a spinster. The licence is on familysearch, but it doesn't give any other details.
The Bennet family are mentioned several times in this will.
Have you researched them? where do they fit in?
Why is Grace Bennet his executor?
I can see some children born of Thomas Bennet and his wife Grace in the 1770s, but not their marriage. Have you found that? was she also a Heywood?
Did Thomas Bennet leave a will? Are there extended family mentioned in it?
There is a will of a Nathaniel Bennet in 1828 from Thelbridge, just a couple of miles from Puddington.
As you no doubt know, most wills prior to this date were destroyed in 1942, so it is difficult to trace people before about 1800.
As to Mary Moore, as you say it's a very common name - and Mary and Betty Haywood are also common, especially when you factor in all the possibilities of spelling - Haywood, Heyward, Hayward, Howard, Heaward. Heawood etc
You would need to try and trace the baptisms of Mary Moore (I suspect this is where the brick wall is). Just go through each possible one - find their families - brothers and sisters; did the father leave a will? Can you rule any of the Marys out by finding other marriages that fit? Are there any other Heywood/Moore marriages?
Sometimes the will of a spinster aunt, or a bachelor uncle can be a wealth of information, and be of enormous help.
Unfortunately in this case it would appear to have been a bit of a red herring!
Although the family you ARE interested in are mentioned in it, and others mentioned in it may ultimately be part of an extended family.