How to add a handling fee on specific items in Shopify?

Hi all-

I sell and ship a few different lines of products to Continental North America.
There is a bit of complexity in our shipping as we have flat rate shipping up to a certain order value & the flat rate and order value(for free shipping) varies depending on where we are shipping to & also which product line.
Also, one of our lines is restricted from shipping to the US.

I need to add a special handling fee for some of our product lines, (because the couriers charge it), one of which ships to both Canada and CONUS, the other of which only ships to Canada. We notify purchasers of this fee on the product page so there’s no surprises at checkout.
Currently we have some rules set up with shopify to address this, but they only seem to work when the free shipping target is reached- The customer gets free shipping, but pays one special handling fee, for shipping. For some reason it doesn’t work below that level. Below the free shipping level, the system charges multiples of the special handling fee, which I don’t want.
The fee needs to be based on final order and not based on products in cart- as it currently appears to be. IE- if someone buys 3 items from the ‘special fee’ product lines, but are still below the ‘free shipping’ threshold, they should only get charged 1 special handling fee & one flat shipping fee.
Currently, they are getting charged multiple times for shipping & handling in that scenario. The handling fee amount would be subject to destination.
If they are above the ‘free shipping’ threshold, they should only pay the handling fee(which the system currently does properly).

I am not interested in any of the paid apps, as I have enough paid apps as it is…

What is the best way to approach and solve this? Can it be done with the shopify system, or?

TIA
TZG