67 Barracuda Carpet Issue

Typically you would lay the carpet out in the sun prior to installation, so I would imagine heat or steam may help in the case of a non-contour fit carpet. Just don't get carried away with either heat source and you should be fine. Some use glue or spray adhesive, but there are varying opinions on that, so you may want to use the search feature here to do a little research first.
The trim pieces you want are called sill plate extensions. They are available to purchase here....https://www.classicindustries.com/product/mp6516.html