You probably have this information already, Giles, but a quick Google search uncovers four items:
1855: A. Whiting, teacher of the organ, piano forte, and vocal music: Also, agent for Brown & Allen's splendid piano fortes. No. 2 Piper's Block, up stairs, Main St., Worcester. ... Also, agent for Taylor & Farley's seraphines and melodeons. ... [4pp.]
1860: Mechanics Hall: Grand concert on May-day evening, Tuesday, May 1st, 1860, by the Worcester S.S. Singing Society, numbering 275 voices, A. Whiting--director, assisted by the National Union Band, M. Arbuckle, leader . [4pp.]
1861: Washburn Hall: Musical soiree. Mr. A. Whiting, assisted by Mrs. Doane, Mrs. Whiting, Messrs. B.D. Allen, Geo. P. Burt, C.C. Stearns, and the Mendelssohn Choral Club, will give a musical soiree on Tuesday evening, March 19, 1861. ... [1p.]
1861-2, The Worcester Magazine: [1861] Amos Whiting lately volunteered his services for a' few weeks in the public schools, with the purpose of giving a juvenile concert to the public on New Year's night. The concert was given and repeated, much to the gratification of those who listened to the harmony of a thousand voices singing the songs that stir the patriot's and the Christian's heart." Evidently the committee favors music, but the expense is still in the way.
In 1862 may be read: "Vocal music, which, for a long period, has annually claimed the attention of the committee, has at length been subjected to the test of a trial. An appropriation of $300 was made for that purpose. It was deemed best that the exercise should be a study rather than a recreation, etc. * * * It was decided to confine the instruction to the high, grammar and secondary schools, the high school to have two lessons per week and the others one of a half hour each; the secondary schools to be taught by a female and the higher grades by a male. Mr. Amos Whiting wa's placed in charge of the higher grades, and Mrs. Wm. Sumner of the lower."
Clues for further searches may be obtained by googling "Descendents of Lady Jane Beaufort," which just may possibly document Amos's parental and grand-parental generations (In both of which Barre, Massachusetts Amos Whitings appear together with a George Whiting). Of course, there were two George Chadwicks composing concurrently in Massachusetts, so the Beaufort angle could be a red herring.