Hi, Lindsay.
Do we know the name of the Borough where Abraham was born?
There is a John Mahood listed in the 1845/1846 NYC Directory at 118 Ludlow. He was a millwright. I do not have access to the 1840 NYC Directory.
I found a Wm. B. Mayhood in the 1940 Borough of Queens City Directory listed at 150-23 116 Ave. Jamaica, Queens, New York. He was a Lumber Inspector. He is the only "Mayhood" listed in all five boroughs of NYC in the 1940 City Directories. The house is still there today and can be seen in Google maps street view (Block 12192 Lot 0078 in the Property Appraiser's database).
City Directories:
http://directme.nypl.org/In the 1940 City Directories, there are ten "Mahood"s listed at different addresses in four of the five boroughs. Queens: George F., Mrs. H.L., Joseph, and Joseph Jr.; Bronx: John A.; Brooklyn: David M., Theo, and Vincent; Manhattan: David M. and Mrs. Millisie H.
I am not sure of the exact date that the 1840 City Directory was compiled, but I know that Abraham was born in March of 1840. I'm thinking that maybe the family moved or were in the process of moving right after Abraham was born and before they were accounted for in the 1840 NYC census or another location.
In order to rule out the 1845/46 NYC Mahood, we will have to look his addresses that was given in the city directory and compare it to the 1840 census for both Mayhood and Mahood because it is possible that the census did not get indexed properly or they were not home at the time the census person came to their house (they could have been visiting a neighbor also). We will also have to look at the very end of the pages to see if they were initially skipped over because they were not home and the census person went back later. I no longer have a subscription to Ancestry.com or access to the Clayton Library in Houston because I moved back to Florida. Thus, I cannot access the census records.
Our only other hope is to go through every Mahood/Mayhood that immigrated to the US and Canada prior to 1840 and rule them out one-by-one.
Jean