Well sound deadening will work. I did it years ago when I was seriously into car hifi
I put some bitumen based roll on sheets under the front footwells and some extra thick underlay type stuff.
Once you then put mats over the top it is seriously good for that point. Rest of car is similar types of thing
I think OP has probably never had to strip and interior to replace the whole carpet though, I mean I havent yet seen a car thats not nigh on all the interior out to be able to get the whole carpet out.
Honestly, get some sound proofing (bitumen type for lower noises, felt type for higher noises). Unclip carpet (remove trim as necessary) in each footwell. Place sound deadening, and replace carpet. Give it a good hoover, buy some decent custom fit mats and your done.