As a Canadian in a happy relationship with an American, we quickly realised the difference that you've pointed out. We also realised that I had a tinge of the stereotypical Canadian "sooorry" sound, so we ran with it. If it's a situation where one of us intends to express remorse for a situation occurring, we slightly intonate towards the "o" sound, and for situations where we're accepting blame, we edge towards the American "sarry" (again, over emphasized to get the point across). It's subtle, but it's worked well for us.
As (yet another) Canadian, I've used the same phonological distinction in my close relationships with Americans to great success. It's been surprising to me how much tension is eased by disambiguating the two senses!
This is apparently called the “Sorry reflex”.
I’ve recently learned that “sorry!” in London at least, can mean - “fuck off/you”.
I would say sorry to someone bumping into me and not realise why but now I understand why.
>> A recent survey of more than 1,000 Brits found that that the average person says ‘sorry’ around eight times per day – and that one in eight people apologise up to 20 times a day.
“The readiness of the English to apologise for something they haven’t done is remarkable, and it is matched by an unwillingness to apologise for what they have done,” wrote Henry Hitchings in his aptly-titled Sorry!: The English and their Manners.