1837 Josiah Heelis ran hotel, livery stable + an auction business in Ramsey (suspect but not checked that means that Constance Radcliffe's book on Ramsey 'Shining by the Sea' will have more about him.
Mathieson has this to say 'By 1820 visitors were better catered for, having a choice between the MANKS ARMS, which had been opened by C. Perry in 1818 near the Market Place, and Mrs. Ryde’s hotel. Four years later there was also Josiah HEELIS’ HOTEL, otherwise known as the THATCHED HOUSE TAVERN. In 1847 Heelis sold this to W. Crawford, who had been chief steward of the s.s. ‘Great Western’ and re-named the house the GREAT WESTERN. By 1851 it had ceased to be either Heelis’ , Thatched House, or Great Western, and had settled down as the ALBERT, which two years later is described as the principal inn of the town. Later still it became the IMPERIAL.'

The two names are found linked in report of a court case in 1836 - see www.manxnotebook.com/fulltext/an1847/p521.htm
Have little on H. Twiss except also appears in advocates note book fulltext/an1847/p092.htm in 1837 (doesnt appear in any directory I can see)