So, one of the benefits of living in this, the Golden Age of Tolkien Studies, is that we're getting very close to understanding the sequence between Tolkien's various works, thanks to tomes such as the Scull-Hammond Chronology (Vol. I of their COMPANION & GUIDE). There are still a few places where it's hazy just where a work fits in, such as FARMER GILES OF HAM (where an equally good case can be made out for its either immediately preceding or immediately following upon THE HOBBIT), but by and large the sequence is coming into focus.
Today in connection with something else I was working on I came across something that might lock down another piece of the chronological puzzle. There are two suggested dates for the little picture book Tolkien drew called MR. BLISS: 1932 or shortly thereafter, or the summer of 1928. The 1932 date was suggested by Humphrey Carpenter in TOLKIEN: A BIOGRAPHY (page 163, ), on the basis that Tolkien bought his first car in 1932 and had several misadventures of his own in driving it (being apparently entirely self-taught as a driver) which in turn Carpenter felt inspired the story.
This date was challenged in 1982, just after the story's first publication, by a letter Joan Tolkien (JRRT's daughter-in-law) wrote to THE SUNDAY TIMES on 10 Oct. 1982, in which she stated that her husband Michael, the Tolkiens' middle son, 'clearly recalled the tale being told to them and it appears in a diary he kept as a Dragon school summer holiday task in 1928'. On the basis of this, Scull & Hammond include it in their Chronology under the entry for '?Summer 1928' (Vol. I, page 146). However, there are two indicators that shows Carpenter was probably right after all.
First of all, in the catalogue that accompanied the display of Tolkien manuscripts in conjunction with the 1987 Marquette Tolkien Conference, Jared Lobdell cites a letter from Christopher Tolkien stating the latter's belief that the handwriting was 'from the 1930s rather than the slightly more florid manner he employed in the mid-1920s (CT to JL, 11 Feb. 1987). Since no one is more familiar with his father's handwriting and manuscripts that Christopher Tolkien, his opinions carry considerable weight in such matters.
Second, in a 1964 letter to Christopher Bretherton (LETTERS pages 347-348), Tolkien notes that he made up the name 'Gaffer Gamgee' during a vacation to Lamorna Cove in Cornwall, near Land's End, and that 'the name became part of family lore'. Scull and Hammond (Chronology page 164) date this vacation specifically to August/September 1932, based no doubt on the account in THE TOLKIEN FAMILY ALBUM, which actually reproduces a photograph from this trip of Tolkien digging in the sand with his children (page 62). This dating becomes significant, because Gaffer Gamgee makes a cameo appearance in MR. BLISS: his name appears on page 37 ('old Gaffer Gamgee is trying hard to hear') and the old man himself, with long beard, wearing a bowler hat, and hobbling along on two canes, is shown in the illo on page 36. Therefore, if it's true that Gaffer Gamgee entered the family lore during the trip to Cornwall in 1932, MR. BLISS as we have it must postdate that vacation.
Given that Tolkien did not finish THE HOBBIT until January of 1933 (if my reconstruction of that work's composition is correct), then MR. BLISS must date from no earlier than the summer of 1933. In any case, it was certainly complete by the fall of 1936, when it was submitted to Allen & Unwin as a possible follow-up to THE HOBBIT (along with FARMER GILES, THE LOST ROAD, the QUENTA SILMARILLION, THE LAY OF LEITHIAN, and other works).