This is an accepted solution.
I'm assuming you've tried https://apps.shopify.com/auto-currency-switcher, right?
Looking at their example store it seems they round to the nearest $.01 (i.e. the nearest cent) which seems to fit your purposes:
If that does not suffice, ping me personally and we can figure something out together.
More than welcome.
Feel free to ping me personally if I can help in other matters as well!