The problem wasn't that I didn't have his parents' names (they were given on his death record), but that I couldn't find any record whatsoever on them.
This turned out to be because George's mother's maiden surname, as listed on the death record, was wrong.
On said record, his parents' names were listed as John Baker and Mehitable Lewis, but each time I looked for them, all I could find was a John BAKER (1792-1861) married to a Mehitable HILTON (1796-1865), both of Yarmouth, Nova Scotia.
I began to wonder if these were his parents, if maybe Mehitable's maiden name was not actually Lewis. After all, how many John Bakers in Yarmouth would have wives named Mehitable-- a name that had been popular about one hundred years earlier, but had, by the end of the 18th century, fallen out of use?
The only evidence that made me think that George was not their son was Mehitable's age: she was born in 1796, and would have therefore been 46 years old when she had him... not impossible, certainly, but unlikely.
While no records can be found for George's birth (or for the births of Canadians in the early to mid 19th century in general), there is a work entitled Yarmouth, Nova Scotia Genealogies, a compilation of genealogical information obtained from George S. Brown's Yarmouth Herald articles between 1896-1910. Unfortunately, this work is out of print, and the only copies available to buy online are almost $200. It is thankfully available to those with a World Deluxe subscription to ancestry.com, however.
John BAKER and Mehitable HILTON are listed in this genealogy, and one of their children is a George. No birthdate for George is given, but it is given that he married an Annie SPECHT in 1862.
George Albert BAKER's wife was Hannah Melissa SPECHT, they married on 24 December 1862-- and "Annie" is a very likely nickname for Hannah.
Provided this genealogy is correct, then Captain John BAKER and Mehitable HILTON were indeed my 4th greats. Perhaps George was, like me, a late "surprise" for his parents.
The question remains as to why George's death record lists his mother's maiden name as Lewis. Well, with death records, it must be remembered that the deceased him/herself is not giving the information. So it's important to consider who is listed on the record as the "informant"-- this is the person furnishing the information on the record to the authorities. In this case, the informant was George's son William, and it's not unlikely that he could have gotten his grandmother's name wrong. Lewis was the maiden name of his great-grandmother on his mother's side, so that may be where he got it from: "Um, I think her maiden name was Lewis..." (clerk jots that down without bothering to ask, "Are you sure that's her maiden name? What if it's not, and 100 years from now your 3rd great-niece has a problem researching your family history because of this?").
I'm very glad to have gotten past this brick wall, because it turns out that there are some seriously cool Mayflower connections on this line...
John BAKER (1792-1861) m. Mehitable HILTON (1796-1861)
George Albert BAKER (1842-1914) m. Hannah Melissa SPECHT (1843-1924)
Jessie May BAKER (1873-1927) m. Thomas Parker SIMMONDS (1871-1953)
Estelle May SIMMONDS (1893-1930) m. Horace William HOWES (1882-1976)
Henry Richard HOWES (1913-1987) m. Dorothy Elizabeth PALMER (1918-1984)
S. HOWES (1937-1999) m. my father (b. 1933)
Me (b. 1974)