One reason a lot of Manx people may have said England is the accent problem and trying to explain the Isle of Man. My wife's Grandmother who was born IOM 1890 had a very strong accent - very much like the Scottish accent, a word I can think of is bush - which she pronounced Boosh.
I am a bit surprised by the lack of BMD records in Texas and Louisiana in the 1860's and 1870's. England/Wales began Civil registrations in 1837, Scotland 1855, IOM 1849, but not compulsory till 1878 ( Marriages 1884)but has the best in the world church records that has been made available free by the LDS IGI, and the poor ex Convict settlement British Colony of New South Wales - now my State of NSW in Australia started in 1856. And more importantly they put all Church records back to 1788 on their records. This is a free search Births to 1918 etc.
After that negativity I had another (Big) look for William Crane and at first found one where his POB was listed in 1850 as Isle Than !!! No wonder I could not find him in 1850. He was in Lockport Niagara 1850/60/70/80/92 , then could not find his death , he changed from Crane to Craine from 1880 , but at the last minute, I found his Naturalization Record which showed he had arrived in the US June 1841 and born November 1824 in Ireland !!! Another example of incorrect detail , he shows his POB Isle of Man on every census, it was transcribed incorrectly in 1850.
Next find was the son of John F Crane, I found him in 1880 in New Orleans with wife Pinkie and two young boys , he gives his and his wife's father as born Ireland, when I looked at the original document to check " Ireland" , it was correct, BUT living next door was his mum (Mom) Allice and siblings Edward , John and Allice. Mother Allice is widowed and the siblings father is shown as born Isle of Man. 1890 census was mainly destroyed in a fire , but I found William again in 1900 in 6th Precinct , New Orleans City Ward 15, with a new wife Bridget and 5 children , including John E , William H and Mary A, this time he states his father was born on The Isle Of Man. This family must be from Mary Ann's brother John Frederick.
Both the Scots and the Manx in the 1800's had a naming pattern that wasn't used 100% , but fairly high use and stayed with the Scot's to the 1900's My parents named their 5 children this way up to 1944 (Me)
The first born male after the Father's father , second after mother's father , third after the father, daughters the reverse.
So this sort of confirms Mary Ann's parents as John Crane and Ann Cannell , I know that Mary Ann should be just Ann. And when they settled in the U.S , the children William, John and Mary have been used , I know in general they are common names , but if it was me, I would be very confident.