***** NOT A TEACHER *****
Hello, E.M.:
I have found some information that may interest you and help you in your decision on how to classify "myself" in your sentence.
Two scholars have expressed their opinion.
I am terrified of violating copyright laws, so I have changed some of their words.
1. The owner himself painted the garage.
2. The owner painted the garage himself.
3. The victims themselves captured the bad man.
4. Wow! I saw the queen herself.
According to those two scholars:
a. Only 1, 3, and 4 represent genuine emphatic uses of those pronouns.
b. Number 2 (which means that "the owner performed the action of [painting the garage] to the exclusion of anyone else") shows the "adverbial function" of the reflexive pronouns.
(i) It is perhaps closely related to: "The owner painted the garage by himself."
*****
The following is only my thoughts:
(1) You know, of course, that "myself" is called a reflexive pronoun.
(2) In "I cut myself," it is clearly reflexive. (One cannot say, "I cut me.")
(3) In "I myself did it," it is clearly emphatic.
(4) In "I did it myself," those two scholars feel that it does NOT qualify as a genuine "emphatic," for it does not directly follow the noun.
(5) But those two scholars do NOT claim that "myself" in a sentence such as #4 qualifies as a reflexive (as in #2).
(6) Therefore, I join the other posters who feel that "myself" in "I baked the cake myself" is an emphatic use of the reflexive pronoun, remembering, however, that it may be an ellipsis of "I baked the cake by myself."
Credit goes to Mesdames Marianne Celce-Murcia and Diane Larsen-Freeman, The Grammar Book / An ESL/EFL Teacher's Course (1983). I hear that there is a new edition with the latest research in grammatical analysis.