Character and meaning for the 四川话 sentence-ending particle 'ga'?
There are many different dialects in China, for many special words in dialects, the "correct" character may not be found (the character has been abandoned in Mandarin), or may be a character but with a different pronunciation from Mandarin, or even can't be found. In fact, the average Chinese person can't tell you what the "correct" character in the dialect is in many cases. We don't care about it when speaking, while in formal writing, we will use another character or words in Mandarin to express the same meaning. Only linguists would be interested in them.
I searched the "ga" on the internet and didn't find a good answer to the correct character. Generally, we will use a character with the same or similar pronunciation to represent it (in informal writing). On the TV here, I find "嘎" is used for "ga". Please note that "嘎" is not the correct character, just for the pronunciation.
What does it mean? Well, your guess is basically right: assertion. More precisely, I would like to say, it is used when:


  you think something (the sentence before "ga") should be right (you are confident about it), but you are not very very sure of it, you need the confirmation from the listener. The answer from the listener is expected to be "Yes!" by you. It is used like "right" as in "we are the best friends, right?"



You example may be good, I think, when "should" shows your mood of guess (I am not an English expert. I know should can show that mood, or show the mood of "order". I think "will" could be more proper here). At last, I want to say that when using "ga", you should have an obvious stop before it. Your example is good in this sense because you have a comma.