Am I correct on both counts below in your opinion? 'I', he said, 'am frustrated.' The comma goes outside the introductory quote (I',) because the original sentence reads 'I am frustrated', not 'I, am frustrated'. But: 'I am frustrated,' he said, 'but I'll get over it.' The comma goes inside the introductory quote ('I am frustrated,') because it is needed to separate two independent clauses separated by a coordinating conjunction. The original sentence is 'I am frustrated, but I'll get over it.' Thank you.
Comma goes inside the speed marks, even when followed up by, he said. 'I,' he said, 'am frustrated.' 'I am frustrated,' he said, 'but I'll get over it.' This sentence is fine as far as I can tell.
And the reason @The Mad Regent is correct is because the comma is present in both sentences, quotation marks or no. The important thing to remember about quotation marks when they are used to denote dialogue is that they are NOT clause boundaries. They only serve to show which part of a sentence is spoken and which part isn't. The attribution (dialogue tag) is an integral part of the sentence, when written with one, not a separate entity. It's only separate if written as a beat, and for it to be a beat it needs to be a complete sentence. 'I,' he said, 'am frustrated.' is syntactically the same as: I, he thought, am frustrated.
Also be aware in the US those would be double quotes, not single. In the EU I take it single quotes for speech are common, but I think here, it would be a tad disconcerting to some readers. Or I'm getting old and inflexible. And I don't know what BrE stands for. Now I have to go look that up. Edited to add, "Oh, OK, now the single quotes make more sense."
I just found this in The Economist Style Guide: When a quotation is broken off and resumed after such words as 'he said', ask yourself whether it would naturally have had any punctuation at the point where it is broken off. If the answer is 'yes', a comma is placed within the quotation marks to represent this. Thus, “If you'll let me see you home,” he said, “I think I know where we can find a cab.” The comma after home belongs to the quotation and so comes within the inverted commas, as does the final full stop. But if the words to be quoted are continuous, without punctuation at the point where they are broken, the comma should be outside the inverted commas. Thus, “My bicycle”, she assured him, “awaits me.” Hence, "I", he said, "am frustrated." is correct, then.
I disagree with the opinion of that style guide. I myself would not follow that advice. But that's me. This style rule they would impose compromises the logical concept of clause boundary, and in an isolating language, if you give up the strictness of clause boundaries then you give up the underpinning logic that makes the whole machine work.
From my above link page 117: This example on the following page is a different circumstance from interrupted dialogue. It's followed by this example which is specific to interrupted dialogue:
Interesting. I wonder if the author is making an error there. It's possible. I can see the comma does break the sentence in my example regardless of the tag inserted in between. And this follows: So it is consistent with your link as well. I do believe you have a point.
It begs another question though, if you are interrupting a sentence with the tag, it feels like a natural pause in the dialogue and thus the comma would belong to the dialogue. At least it sounds that way to my ear. Perhaps one shouldn't put the tag in the middle of a spoken sentence at a place it does not normally pause. Though I can see this is a circular argument. When you interrupt the sentence with the tag, the tag serves as a pause for emphasis. So if you didn't insert the tag and you wanted the pause for emphasis, what punctuation would go there? An ellipses I would think. “My bicycle ... awaits me.” “My bicycle ..." she said, "awaits me.” Interrupting the sentence with the tag could be said to create the need for the dialogue to own the comma. And around and around we go. Nice brain exercise anyway.