Sociological mimicking. You begin to mimic the speech patterns you hear. I noticed the slight difference in accents of relatives (Polish-American) who lived in a small town a scant 30 miles away from my relatives (also Polish-Americans) who lived in the same little town as myself. A slight difference despite the fact that they were my aunts and uncles who were actually brothers and sisters and had lived apart for twenty-thirty years. So yes, I agree with your observation that it is likely "local influence".

The regional variations existed before Europeans got to America.

Ingrained in my Mind! I was in England a few years ago in a Hostel with various persons from abroad. I met this beautiful person from Spain whom which I conversed with without a problem. She inquired to the fact that she could read and write English without any problems but could not understand it when it was spoken to her. Now I want to relate that we had absolutely no problem conversing at any time and I explained to her that it was accents that was because of the various accents that accentuate in a Country so large and diverse. Being I reside in Maryland between Pa. and WV it is very apparent and I myself have to sit back and rethink what is being said.

All languages are dynamic to one degree or another. They tend to change even in areas where the people are isolated from external input. There can be external forces at work driving changes in language as well. It would be extremely difficult to find a single or main cause for the changes that occur except in obvious circumstances.

American English is massively influenced by African syntax. Not to mention Spanish that is pervasive in the colonial states out south west. If a language is living it will have linguistic drift. There is no correct pronunciation. There is correct grammar, The Queen's English, how we pronounce it here. Latin does not change. It is dead. Like the Republican Party here in the USA.

Even the 'English' accent has changed. Language, dialect, accent are constantly changing. If I remember the article correctly it is largely driven by young women. Also driven by those in power. So if a prominent member of court has a speech impediment or says a word incorrectly or garbled, then rather than being correct that mode of speech will ripple out from there.

Time of settlement, geographic regional dialects of the immigrants, social stratification within the new societies...
What I find really interesting is that the US ended up with a large number of regional dialects/accents, whereas Australia has virtually none. Australia has social stratification of accent (poor/rural more nasal, urban/wealthy more anglicised) but people from similar backgrounds will sound virtually indistinguishable, even if they were brought up thousands of miles apart.