I would suggest that Charlotte may want to have a look at the Cunard White Star Lines Archives, which are held by the Harold Cohen Library, in Liverpool.
They are very detailed and there may well be information regarding these ashtrays still in the archives.
As to the date, one may need to be cautious. They could, as you say, date to the five years before the ship was converted to serve as a troopship in the Far East, but could just as easily date to a post-war refit. The QM, was launched in 1934, but fitting-out took the best part of two years, only making her maiden voyage in 1936. If these are from that original period, then design and supply of the ashtrays is a three year period from 1934 -1936. It is unlikely that they were ordered before that, as the ship very nearly remained uncompleted, but for goverment intervention.