I have no real knowledge of the subject and will almost certainly not be able to help, but I'm curious about the question. Why not just put it out and see if anyone can answer?
Question 1: does anyone have a satisfactory definition of "grapheme"?
The tightest definition I found via internet searching is on
this page, and is due to "David Crystal":
Graphemes are the smallest units in a writing system capable of causing a contrast in meaning. In the English alphabet, the switch from cat to bat introduces a meaning change; therefore, c and b represent different graphemes. It is usual to transcribe graphemes within angle brackets, to show their special status: <c>, <b>. The main graphemes of English are the twenty-six units that make up the alphabet. Other graphemes include the various marks of punctuation: <.>, <;>, etc., and such special symbols as <@>, <&>, and (£). . . .
Question 2: What if anything is wrong with the following analysis?
I find Mr. Crystal's definition unsatisfactory. Following the definition, one might consider individual Chinese characters to be graphemes in most or all cases. Indeed, we have
here a list of standards for 4700+ common characters published under the title of "List of graphemes..."
For example, the character "帥" (handsome) is capable of causing a contrast in meaning. According to the published list I referenced above, it should be a grapheme.
If we modify that character by adding only one horizontal stroke (一) to the top of the right half of "帥", we get a character "師" (teacher, instructor). Presumably this stroke is a "smaller unit" than a whole character and it is definitely capable of causing a contrast in meaning, so under Mr Crystal's definition it seems that 師 or 帥 is not a "grapheme" at all. Only the extra stroke (一) would seem to meet that definition.
In Chinese, sometimes the smallest such unit is going to be a single stroke. Other times it's going to be a larger structure that still doesn't necessarily constitute a character (generally, 部首). There are also cases in which a full character could meet the definition (e.g., 口). I'm thinking the concept of "grapheme" might just be a sloppy idea resulting from excessive reliance on western languages/thought and/or lack of imagination among the people who invented it. It's also possible that there are superior definitions out there to Mr. Crystal's.