EDIT: not sure from your last post if you have already mounted the new treads you purchased just yet bit in case you haven't yet:
How much dirt time have you had with the duratracs already on your truck? I'm a fan of the duratracs and have run them on my midsize crew cab for 9 years (2 sets), and put them on my 2020 F-150 crew cab that I just purchased in August.
Before going all duratrac all the time, I ran MT's on my midsize crew cab and while they gave me the bite I needed off road, they were very loud, even for me, and I can barely hear out of my left ear. Once I switched to duratracs, I got the bite I needed but they have much better road manners, especially at freeway speed compared to the MT's I was running. I spend a lot of time in the winter in the Sierras near Tahoe and I found the duratracs were very good in the snow as well.
I would say if you haven't already, put those 31" duratracs through some solid off road trips and see how they treat you. You may be surprised with how well they may fit what you are looking to do. You might not have to spend a dime on new tires, or re-gearing, or speedo calibration, or wheel well trimming, or many of the things that come with running bigger more aggressive tires. I've went the big tire route, and it isn't as simple as a lift and a trip to the tire shop. You'll need to get a full size spare with the same size tire you plan to upgrade to, so that's 5 tires you need to buy. Then you will need to figure out how to carry that spare tire if it won't fit under the bed which will most likely have you throwing that spare in the bed, with a chain wrapped around it, and taking up valuable real estate. This is on top of loss of MPG, speedo issues, possible re-gearing, trimming and tire rub. Take it from a guy who has been through all this many times over.
Sorry for the long rant, but give those 31's a good beating in the dirt, they might just do the job and you can spend your money on other things. After doing this for over 20 years, I've learned to put less importance on lifts and big tires, and more investment on how to carry things, making the rig as reliable as possible and the actual gear I use to live while outside.