I'm a direct line descendant of John Ingamells and I spent several years trying to definitively tie him in with his parents. Although Ingamells is a pretty uncommon name around the country, unfortunately there are hundreds in Lincolnshire. However, that being said, there still weren't that many in one area when John was born. Plus the Ingamells tended to have more females than males, and not many of these males survived to have children, so there are fewer possibles than you might think.
There were 3 particular men surnamed Ingamells who married (at Sibsey) to 3 sisters surnamed Burr originally from Algarkirk; so I'm firmly of the opinion that they are closely related. John, William, and Christopher Ingamells who married Elizabeth, Mary, and Ann Burr respectively, fit in with being the sons of William Ingamells and Ann nee Green.
John's baptism in 1727 has his parents as William and Elizabeth Engoldmell, however I think this is an error. Mumby registers appear to be written out at the same time for the whole year; the layout and handwriting is too consistent. An entry for the same day has a mother Elizabeth, and I think it entirely possible that someone took that mother's name mistakenly from the line below when copying from the rough register. There is no other couple of William and Elizabeth Ingamells (whichever spelling) at the time.
William senior is shown as being of "the Chapple" from his burial, and this is Mumby Chapel aka Chapel St Leonards. William and Ann's children were baptised at Hogsthorpe, Mumby, and Addlethorpe; all of which are within a few miles of each other. Addlethorpe is only about a mile from the village of Ingoldmells, which is the source of the surname. Goodness only knows where someone got Germany from, but that's been floating round on Familysearch for donkey's years - so I'd advise you to ignore it.
I can take the Ingamells line back several more generations, and they end up in c1500 in the Great Carlton area which is about 16 miles or so north of Mumby. Remember that the place names on the east coast are often derived from Scandinavian names due to the invasion tendencies of the Vikings etc, so there will be similarities with names in other northern European countries.