I'm delighted to hear from you.Unfortunately I can't make all the connections you would like but perhaps I can clarify a few.(I don't have nay information on what year my family arrived in Herkimer County.It was at least in time for my great, great grandfather to fight in the Civil War).
Referring to the 1896 Herkimer Co. Directory, Christopher and Frederick Heidel were Brothers who allegedly were both born in Saxony in 1839 and 1836 respectively.Although I couldn't swear to it, I assume the teacher Charles, is Fred's son born in 1873.Edward may be a son of Christopher whom I have found referred to as EDwin born in 1871.
I'm not too much help on who went west because my grandfather went east to Vermont.I do know however that someone went west because in the early 1920s my grandparents and my mother took a couple years touring the country and I recall my mother mentioning visiting various uncles and families en route, at least one which i believe was in California.But I don't think this sheds a lot of light on Kansas and Wisconsin.
I do hope, however, it's a little help and I'd be delighted to hear if you should have more to add regarding the Heidels of Ohio, Herkimer Co., New York.