Disclaimer: I know that modern sound deadening materials are most likely superior to the stuff originally installed in our cars. I wanted the overall cabin-feel of the car to be as original as possible.
There is not currently original-style sound deadener available for Cougars. The closest you will get is a 1/8 inch thickness mastic tar mat kit from Auto custom carpets ACC, available from WCCC and RockAuto (my choice - cheaper). This leaves a lot to be desired if attempting to be closer to original. So, I set out to recreate the factory sound deadener.
I purchased two 7 piece kits from Rock Auto (link below) and sourced a 40oz roll of jute padding from Rex Pegg Fabrics in Phoenix. I bought 7 yards but probably used half of it. I traced and cut out pieces of jute to be sandwiched between the two tar mats. I used DAP Weldwood contact adhesive in a paint spray gun to spray the glue, the most technical part of the project. I found a new (old) craftsman paint gun at an estate sale and had purchased a gallon of DAP for other interior projects such as installing my headliner. Glueing the deadener together used quite a bit of glue. The end result was a 3 layer sound deadener pad that is .48 inches thick.
I am happy with the results and are in process of installing the carpet.
A word on carpet - I purchased the mass backed loop carpet from RockAuto. I had to trim some of the glued on padding on the driver side toe kick to allow for full accelerator pedal travel. Additionally, mass backed carpet makes installation a bit tough as the added thickness makes installing the door sill plates very tight.
Sound deadener link
https://www.rockauto.com/en/moreinfo.php?pk=5999928&cc=1366264&pt=14534&jsn=605
Jute padding
40oz. Jute Pad - 40oz. Jute Pad - Rex Pegg Fabrics