Does FunnelKit Stripe allow the user to move the Express Checkout buttons for Apple and Google to the Card section of the checkout page?

Yes, it does. For this, after setting up the FunnelKit Stripe plugin, navigate to WooCommerce ⇒ Settings ⇒ Payment. Then, Manage Stripe Gateway. 

Now to add Google Express checkout to the Card Section check “

Enable Google Pay”, set the Google Merchant ID. 

Now, it will appear on the inline with a credit card. 

Similarly, you can switch to the Apple Pay tab and enable the Inline option.