This is so right!
Unless you have a VERY heavy accent, I wouldn’t stress about trying to change it too much. As Malamute said, more often than not Americans absolutely LOVE hearing a different “exotic” accent. Forcing yourself to sound like an American never works, you more often than not, just end up sounding like Gru from Despicable Me, and even if you happen to nail the accent you’ll almost certainly trip up on the American words, phrases or names. Best stick to what you’re comfortable with and own it! Make it your own and embrace your “foreignness”.
Whenever I have mentioned to friends, colleagues and even complete strangers that I forget just HOW different I sound and that I probably should work more on sounding more “local”, they quite literally beg me not to. They really do love hearing the different “exotic” accent and love that we use different “fancy” words for almost everything! I’ve had at least half a dozen people ask me to record voice mail messages for them to impress their friends. My wife’s entire office and nearly all of her 30 staff members now naturally say things in conversation like “dodgy”, “crap”, “rubbish”, “lovely”, “just now”, plus a litany of random Afrikaans words and a whole bunch of very British ones too. I’ve even noticed that the vocabulary of our friends and colleagues has improved dramatically over the years and in some cases expanded. It is truly quite amazing what a little bit of diversity can do.
Most important though, is just being understood. 99% of that is just using the American English words instead of the British English words. You simply don’t realize just how many words are different, until you have to actually use them to be understood. I used to think American English was only slightly different, maybe 30-50 words and then some slightly different spellings eg. “z” instead of “s”, “color” not “colour”, “aluminum” not “aluminium” etc. Not even close! In some ways it really is a completely different language. The weird thing is that growing up with American TV, Music, Movies and media we already know almost all of these names and words, we just never used any of them.
The best part of having an accent is that you get a LOT more slack and people are generally a lot more forgiving, receptive, understanding, and considerate. It’s like playing stupid, instead you still come across as intelligent, only different. I once got out of a traffic ticket because I sounded foreign and the officer cut me a break because I accidentally said kilometers instead of miles. Hahaha! Also, whenever i’m dealing with people in customer support, banks, information desks, reception, on the telephone, etc. and don't quite know the procedure, need help, or just have a question, I just say something in my best South African accent like, “Excuse me. You might have noticed, but l’m not from around here... and I really have no idea how this is supposed to work...” and they laugh with genuine delight and more often than not make a concerted effort to explain things in great detail, go out of their way to be as helpful as possible, and often cut you some serious slack, when they’d normally cut off or shut down the average customer. It really is like a secret weapon in many cases.
Your accent will naturally change over time as you learn to stretch out your words and slow down your speech. The hard ‘g’s and rolling ‘r’s will soften, and the quick and flat “a”s will become more accented and drawn out with time and you’ll start to naturally pronounce many words and names the American way, especially the American ones, which you’ll use more and more. So much so that your South African friends and family will start commenting that you “...sound so American!”
I realized just this on our recent visit to SA this April. I was talking to my daughter on a swing in Durban (where I grew up) and the mother next to me turned around and asked me where I was from! The exact same question I get almost every single day (sometimes 5 times a day) in the US. That’s when I realized than I now officially have an accent without a home, as I like to say. I sound foreign to Americans and I sound foreign to South Africans. Hahaha!
In short... just be yourself. Embrace your accent and incredibly unique foreignness. Unless you are intending to act in Hollywood or host a TV show, going full Charlize Theron is just a complete waste of time, effort and money. If anything, it might even work against you, as you’ll often be treated like every other American. Unless they already personally know another South African, the vast majority of Americans effectively have absolutely no preconceived ideas or stereotypes associated with South Africans. Especially negative ones! Unlike, they do for so many of the other larger immigrant populations that they might otherwise perceive in a negative way. This lack of preconceived ideas tends to make them more accepting, welcoming, friendly, and genuinely curious towards us. And that goes a really long way in most cases.