I would like users to be able to:

For example, say my site is in euros, and there's a monthly subscription for 100€. And currently the exchange rate makes 100€ = $110 USD. I want a US person to see $110 USD on the product, then $110 USD at the checkout page, then get charged exactly $110 USD every month.

Some evidence that shoppers prefer to see prices in their own, familiar currency:

Shopify: 92% of shoppers prefer to make purchases on sites that price in their local currency and 33% are likely to abandon a purchase if pricing is in U.S. dollars only: https://www.shopify.com/enterprise/blog/multi-currency#:~:text=92%25%20of%20shoppers,S.%20dollars%20only

From the Shopify page:

“In the first 45 days of our first year with Shopify,” says Julien Plouffe — CEO at Moonglow Jewelry, “we shipped to 84 countries. During the same time the year before, we had only shipped to 20 countries. International visitors just weren’t converting once they reached the cart page. Allowing buyers to see our products in their local currency gave them the confidence to finish their checkout instead of dropping out.”

WinSavvy: Currency personalization increases average order value by 13%: https://www.winsavvy.com/revenue-uplift-from-localization-and-currency-personalization/#:~:text=Currency%20personalization%20increases%20average%20order%20value%20by%2013%25

Lingo-soft: Currency localization alone has been shown to boost conversion rates by up to 12%: https://lingo-soft.com/the-role-of-localization-in-e-commerce/#:~:text=Currency%20localization%20alone%20has%20been%20shown%20to%20boost%20conversion%20rates%20by%20up%20to%2012%25.