Using "so" at the end of a sentence without an ellipsis

In American English, we often add a drawn out "so" at the end of a sentence to imply an outcome.

Example:

Jane wanted to go out, but I was tired, so we didn't.

Rather than say "we didn't" at the end, we often simply end the sentence with "so." When we do that, we see people reflect that in writing by adding an ellipsis to represent the missing words and the pointedly pregnant "so."

Example:

Jane wanted to go out, but I was tired, so...

However, recently I visited Ireland -- County Cork to be specific. Speakers there do something similar, but they've cut to the chase. Rather than linger on the "so" like we Americans do, they seem to simply end the sentence with "so" and move right onto the next. It's almost like "so" becomes a pronoun for all they left unsaid that we could readily infer.

Example:

Jane wanted to go out, but I was tired, so. Besides, I didn't have the money anyway.

This made me question how I normally write sentences like this, question using the ellipsis.

My question is this:

Is it grammatical to end a sentence with a single period after "so" like I did above without having the coordinate clause explicitly follow it?

On one hand, we imply things all the time and grammar takes it completely in stride. But on the other hand, it looks awfully odd ending a sentence with a coordinating conjunction like that. Yet I can't find any rule that prohibits it. So I cast my bread upon the waters.

Your examples are dialog. As such, it's "grammatical" to describe exactly what was said.

If you are quoting an American, it's just fine to say "Jane wanted to go out, but I was tired, so...". The same is true for County Cork.

Spoken language plays fast and loose with the rules of grammar people worry about for text, but if you are quoting dialog, I think you are fine.

I would say, however, that if you are writing for an AUDIENCE of one kind or another, I would use the form most understandable to them if there is any ambiguity. American English uses "so" at the end of a sentence, with a full stop, more often in the concept of "just so." You're stating that something is EXACTLY as expected or described previously, and a hasty reading could come off as confusing.

If you are transcribing dialog, transcribe what they are saying. If you are not transcribing dialog, use the form expected by your expected audience.