Right folks this should put some more dates on this.
1891 UK census has him living in North Sheffield. Butcher, lodger with a James Haller, same age, occupation and both born Germany.
1897 JAS has UK birth record for his daughter Elsie R. L. Uebel in Hull area.
1901 UK Census has him living Holy Trinity, St Mary’s, Yorks (Hull area). Wife Sophie, daughter Elsie and 6 month son Ludwig. It looks like the 2 other children listed on his UK naturalisation (Hannah Sophia and Henry Carl have died).
So the US period must have been between 1891 and 1897.
So far can’t get anything definite for UK departure, US arrival or the return leg.