Hey folks!
Oliver - you've got the best solution so far.
The big kicker here is that PayPal Express is a checkout process in and of itself, so it replaces your Shopify checkout entirely, except to confirm the order placement.
Using an integrated payment gateway like Stripe (or most others) along with your PayPal Express will help, but if they go through the checkout process and then choose to pay with PayPal Express, they're going to have to re-enter their payment info. It's not a perfect flow, still, but give it a little while and you can make an educated decision on what is best for your customers.
Hope that helps!
Dylan