Hm, it seems the Handling charge for FatFreeCart does indeed work as you described, on a per-product basis rather than per-order.
Since we don't offer support for FatFreeCart, we on the E-junkie support team aren't actually that familiar with how it works or how it differs from the E-junkie cart, so in this case we can only suggest experimenting with different approaches to see if you can get GC shipping charges to apply to FFC orders.
E.g., you might try deleting all shipping-related fields in your FFC button code, so no pre-calculated shipping amount is passed from the cart to checkout, but that might not indicate it's a tangible-goods order eligible for shipping, so in that case, try leaving just a token Handling amount per item and see if you can tack Shipping charges onto that at GC's end.
