Is there a hard rule for where commas go when there seems to be two independent clauses but there's only one subject?

Question: "Is there a hard rule for where commas go when there SEEMS to be two independent clauses but there's only one subject?"

If there are two independent clauses there have to be two subjects, since two subjects and two verbs are the minimal requirements for two independent clauses joined in whatever manner by conjunctions, these are compound sentences. Traditional grammar does use a comma here for these compound sentences containing a conjunction:

You can leave now, or you can go later.

BUT:

You can leave now or go later. [two verbs, same subject]

compound sentence

Sample sentence: "To put it simply, I'm going to go to the store, and then I'll visit Mary."

Point One: That is an example of two independent clauses: the first is: "I'm going to the store" and the second is "I'll visit Mary". There are two subjects and they are both the pronoun "I". As already stated, traditional grammar does put a comma between them. In general, two independent clauses are joined by conjunctions like "or" or "and" or "but" etc.

Sample sentence stated differently:

"To put it simply, I'm going to go to the store and then to Mary's house."

Point Two: Now, the phrase "To put it simply" precedes the sentence and does call for a comma. Anything idea expressed by a phrase or even a single word such as an adverb that comes first, does need a comma.

Truthfully, I never thought it was a good book.

I never truthfully thought it was a good book.

Point Three: Had the sample sentence been:

"To put it simply, I'm going to go to the store and then the gym", that would be a complex sentence (two predicates) and also does not call for a comma. It has one subject and verb and two predicates joined by "and".

Point Four: When you have a complex sentence with a subordinating conjunction (which makes for a complex sentence), it has to be placed correctly:

He had a big heart since he was raised that way.

BUT

Since he was raised that way, he had a big heart.

To simplify, when you have an independent and dependent clause, if the dependent clause precedes the independent one, you need a comma:

She did not want to date him even though she found him attractive.
Compared to:
Even though she found him attractive, she did not want to date him.

complex sentences

Finally, (am I repeating myself?) there is a difference between sharing a subject and having the subject stated twice:

They left early and got lost [complex sentence]. versus: They left early, and they got lost. [compound sentence]

"A coordinating conjunction joining two independent clauses creates a compound sentence and requires a comma before the coordinating conjunction."

coordinating conjunctions and two independent clauses

Advice: make sure of whether your sentences are two independent clauses, both of which must have a Subject and Verb or Subject Verb and Predicate, in which case you need a comma before the coordinating conjunction VERSUS a dependent and an independent clause which may or may not need a comma depending on how it is stated. (See the example with "lost" above).

That said, with transcription, things can get dicey. There are no rules here other than the transcriptionist's ability and skill in hearing speech. I have personal experience of this, as I am an interpreter (legal) and have to deal with deponents all the time. Many times, speech is halting, truncated, filled with filler words, hesitation, and repetitions, to name a few. These are often punctuated in ways one would not see in traditional dialogues or speech formats. (And often, the lawyers can get really annoying because they are looking for black-and-white, clear speech, which most times is never what the deponent gives them, unless they ask for a yes or no answer.)

For instance, one uses square brackets for things like inaudible or unclear: [inaudible] or even a question mark [?]. Also, ellipsis is common where speech trails off.... Within an utterance, the ellipsis can indicate a pause and at the end (terminal ellipsis), it can indicate trailing off.

All this said, transcription is actually more of an art. There are choices to be made by the transcriptionist and that will largely depend on education, experience and cultural knowledge. Also, transcribing from a tape and in person also is not the same "exercise". Transcribed speech will never be some clean, antiseptic grammatical exercise. It is a messy business by definition and the transcriptionist (and the interpreter) does their best to render the meaning provided by a deponent. In fact, in depositions with interpreters, the transcriptionist is actually taking down what the interpreter says. :)

One awful example I can contribute: I had a deponent that was functionally illiterate in her mother tongue and English. When asked what the weather was at the time of the accident, she said, supposedly in the language I was interpreting: shhkno estor. I had to stop the proceeding and ask her: She was saying snow storm and I was simply unable to "get it", as I was listening for Spanish. Ah, life is good and interpretation's a bitch. :)