I've been digging in the Welsh Newspaper archive instead. 1873 is the earliest I can find for either address - not sure if that's because of the newspaper on the Welsh database, or that's when they were newly built
No 2
I can see an HH Davies in 1873, and a George Siddons in 1879. The former isn't easy to track down. The latter is still in Caernarvon in 1881, an unemployed schoolmaster living with his wife & schoolmistress sisters in law (all from Yorkshire)
No 12
May 1875 - Mr. J. C. Getley, North and South Wales Bank (wife has baby)
Sept 1875
NORTH WALES TRAINING SCHOOL OF MUSIC, 12, UXBRIDGE SQUARE, CARNARVON.
PROFESSOR: MR JOHN HENRY ROBERTS (PENCERDD GWYNEDD), Pupil
of Sir W. Sterndale Bennett, Mus. Dr., M.A., D.C.L.; Associate of the Royal Academy of Music, London; Local Examiner, by appointment, of in- tending candidates to the Royal Academy Holds a first-class diploma from the above Institution; Composer of the Chief Prize Musical Composition, Cantata, "The Gorsedd Ode" at the Bangor Royal Eisteddfod, awarded twenty Guineas and a Gold Medal.
THIS SCHOOL has been established for the purpose of encouraging the study of music in the Principality, and of enabling ladies and gentlemen to obtain sound Musical Instruction. The Branches taught include- PIANOFORTE HARMONIUM ORGAN SINGING HARMONY COMPOSITION
The system of teaching is based on that of the ROYAL ACADEMY- OF Music LONDON. Composers Every advantage will be given to students anxious to excel as Pianoforte-players, Singers, and composers.