Thanks for the video! It is kind of deceptive in the video it doesn't seem too bad, but you can tell it is a little loud. Is there an odd vibration coming from the shifter, sounded more metallic? I think like you said, you have the truck, spend a little money on it and see if it starts becoming a little more to your liking.
I would start with unbolting the front 2 seats, and shift console and center console, should be a total of about 17 bolts. 4 on each seat, 5 on the center console and 4 for the shift console. The transfercase knob just unscrews and you need to put the shifter in N and the shift console lifts out. Then the dead pedals on both sides and threshold caps, then pull the carpet back.
Get good solid products like:
Sound Deadeners Showdown Tiles -
CLD Tiles™ | Sound Deadener Showdown
Second Skin Luxury Liner Pro -
Luxury car quiet with our noise insulation products Luxury Liner™ Luxury Liner Pro™ | Second Skin Audio, Made in the USA.
Second Skin Spray Adhesive -
High Temp Spray Adhesive
Clean up the area as high up on the firewall as you can reach and as far back on the floor as you want to go. Lay down the Sound Deadener Tiles, be thorough and cover it all. Use a wooden roller to press it hard to the floor.
Clean up the metal backing on the tiles with alcohol and then spray the adhesive on the tiles and Luxury Liner Pro and get it as far up on the firewall as you can and as far back on the floor as you want. Couple of things to be careful about, watch the thickness around the pedals, dead pedals, bolt holes for the seats and thresholds.
Button everything back up.
Open the hood and pull the hood lining, make sure you have extra push pins on hand because they will certainly break. Clean under the hood and cover under the hood with Sound Deadener tiles.
The more time you take cleaning things up and getting the best coverage possible will determine how good it helps with the noise.
I would start there, probably cost you about $150-175 and a day or two on a weekend. But could be a big determining factor on whether you can quiet the truck down to something you want to live with. If this helps, then I would start looking at the mechanical aspect with the vibration dampener and engine mounts.