Hi,
Ah I see, that's because you are redirected to the checkout when you add a product to the cart, so in that case, the only possible payment method is selected at that point.
Try to change the "when a product is added to the cart" setting to something else in order to not be redirected to the checkout directly.
That way, when you access the checkout with both products in the cart, it should work fine.
That's however not a foolproof solution so I don't recommend doing that.
A more complex customization of the code of the payment view would be necessary to check each payment method, hide the correct one all the time, and select the only one possible. That will it would work all the time, regardless of how you configure that "when a product is added to the cart" setting or what the customer do. But in that case, it's more complex than a 1 line code modification and will require a developer to spend some time customizing the code for you.
I don't see how changing something in the warehouse would do the trick though.